How to graph the following summation/integral function?

Hello,

This function has summation and integral elements. I am trying to graph / plot this function.

I have already wrote working code for this function with the upper limit as 50.

>>  syms n t
Q = @(v) sym(v);        %convert to rational
Pi = sym('pi');
f1 = Q(0.111627907);
f2a = int((Q(-0.3072*10^(-6))*(t - 25)^4 + Q(1.2))*cos((2*n*Pi*t)/860), t, 0, 50)
f2 = symsum(1/430*f2a*n*Pi*t/430, n, 1, 50)
f3a = int((Q(-0.3072*10^(-6))*(t - 25)^4 + Q(1.2))*sin((2*n*Pi*t)/860), t, 0, 50)
f3 = symsum(1/430*f3a*n*Pi*t/430, n, 1, 50)
f = f1 + f2 + f3;
f=f+860  %causes the function to repeat for a period of 860

I have attempted to graph this using the following code:

t = 0:10:1000;
y = f
plot(t,y)

However, MATLAB gives this response:

f2a =
 
(43*(1384100138017444386099000000*pi*n - 23806522373900043440902800000*sin((5*pi*n)/43) - 779757153651435678125000*n^3*pi^3 - 779757153651435678125000*n^3*pi^3*cos((5*pi*n)/43) + 40235469128414080991250000*n^2*pi^2*sin((5*pi*n)/43) + 102003116029984338644329*n^4*pi^4*sin((5*pi*n)/43) + 1384100138017444386099000000*n*pi*cos((5*pi*n)/43)))/(9444732965739290427392*n^5*pi^5)
 
 
f2 =
 
(t*(34602503450436109652475000000*pi - 23806522373900043440902800000*sin((4*pi)/43) + 12183705525803682470703125000*pi^3*cos((4*pi)/43) + 25147168205258800619531250000*pi^2*sin((4*pi)/43) + 39844967199212632282941015625*pi^4*sin((4*pi)/43) - 12183705525803682470703125000*pi^3 - 34602503450436109652475000000*pi*cos((4*pi)/43)))/(15864199903390214389760000000000*pi^4) - (t*(81476824985038514007281250000*pi^2*sin((10*pi)/43) - 23806522373900043440902800000*sin((10*pi)/43) - 71055370626487076169140625000*pi^3*cos((10*pi)/43) - 62284506210784997374455000000*pi + 418276527670454528653401605625*pi^4*sin((10*pi)/43) + 71055370626487076169140625000*pi^3 + 62284506210784997374455000000*pi*cos((10*pi)/43)))/(166536024905829114577944576000000*pi^4) - (t*(27199177130807918750085000000*pi^2*sin(pi/43) - 23806522373900043440902800000*sin(pi/43) - 13705011732577633478725000000*pi^3*cos(pi/43) - 35986603588453554038574000000*pi + 46612975950918123136330889104*pi^4*sin(pi/43) + 13705011732577633478725000000*pi^3 + 35986603588453554038574000000*pi*cos(pi/43)))/(18558870054532215324095912345600*pi^4) - (t*(3830946895889503486628125000*pi^3*cos(pi/43) - 23806522373900043440902800000*sin(pi/43) - 23529702346296554563683000000*pi + 11628050578111669406471250000*pi^2*sin(pi/43) + 8519402253940321947913002409*pi^4*sin(pi/43) + 3830946895889503486628125000*pi^3 - 23529702346296554563683000000*pi*cos(pi/43)))/(3391984230735498485880691097600*pi^4) - (t*(36211922215572672892125000000*pi^2*sin((21*pi)/43) - 23806522373900043440902800000*sin((21*pi)/43) - 21053443148588763309375000000*pi^3*cos((21*pi)/43) - 41523004140523331582970000000*pi + 82622523984287314301906490000*pi^4*sin((21*pi)/43) + 21053443148588763309375000000*pi^3 + 41523004140523331582970000000*pi*cos((21*pi)/43)))/(32896004919669948558606336000000*pi^4) + (t*(58132205796732664216158000000*pi - 23806522373900043440902800000*sin((5*pi)/43) + 57770647999727566520925000000*pi^3*cos((5*pi)/43) + 70975367542522438868565000000*pi^2*sin((5*pi)/43) + 317402688138038146622203971984*pi^4*sin((5*pi)/43) - 57770647999727566520925000000*pi^3 - 58132205796732664216158000000*pi*cos((5*pi)/43)))/(126373292499404074382742100377600*pi^4) + (t*(56748105658715219830059000000*pi - 23806522373900043440902800000*sin((10*pi)/43) + 53741642786810598372053125000*pi^3*cos((10*pi)/43) + 67635823604864070146291250000*pi^2*sin((10*pi)/43) + 288236427156004574751937759369*pi^4*sin((10*pi)/43) - 53741642786810598372053125000*pi^3 - 56748105658715219830059000000*pi*cos((10*pi)/43)))/(114760799701001819146809874841600*pi^4) - (t*(33838029536996242113641250000*pi^2*sin((16*pi)/43) - 23806522373900043440902800000*sin((16*pi)/43) - 19017497220404864753790625000*pi^3*cos((16*pi)/43) - 40138904002505887196871000000*pi + 72144865908803353020699659449*pi^4*sin((16*pi)/43) + 19017497220404864753790625000*pi^3 + 40138904002505887196871000000*pi*cos((16*pi)/43)))/(28724344759986519612937836953600*pi^4) + (t*(6920500690087221930495000000*pi - 23806522373900043440902800000*sin((18*pi)/43) + 97469644206429459765625000*pi^3*cos((18*pi)/43) + 1005886728210352024781250000*pi^2*sin((18*pi)/43) + 63751947518740211652705625*pi^4*sin((18*pi)/43) - 97469644206429459765625000*pi^3 - 6920500690087221930495000000*pi*cos((18*pi)/43)))/(25382719845424343023616000000*pi^4) - (t*(91737649369937756095728125000*pi^3*cos((13*pi)/43) - 23806522373900043440902800000*sin((13*pi)/43) - 67820906762854774918851000000*pi + 96605361377322208459991250000*pi^2*sin((13*pi)/43) + 588027665292769745401166463529*pi^4*sin((13*pi)/43) + 91737649369937756095728125000*pi^3 - 67820906762854774918851000000*pi*cos((13*pi)/43)))/(234122125996195356939015264665600*pi^4) - (t*(29331656994613865042621250000*pi^2*sin((6*pi)/43) - 23806522373900043440902800000*sin((6*pi)/43) - 15347960055321208452534375000*pi^3*cos((6*pi)/43) - 37370703726470998424673000000*pi + 54208637986090906913480848089*pi^4*sin((6*pi)/43) + 15347960055321208452534375000*pi^3 + 37370703726470998424673000000*pi*cos((6*pi)/43)))/(21583068827795453249301617049600*pi^4) + (t*(51211705106645442285663000000*pi - 23806522373900043440902800000*sin((13*pi)/43) - 39497039103906171404065625000*pi^3*cos((13*pi)/43) + 55082357236798876877021250000*pi^2*sin((13*pi)/43) + 191170261941871478097994282969*pi^4*sin((13*pi)/43) - 39497039103906171404065625000*pi^3 + 51211705106645442285663000000*pi*cos((13*pi)/43)))/(76114085773152531432773097881600*pi^4) + (t*(1384100138017444386099000000*pi - 23806522373900043440902800000*sin((5*pi)/43) - 779757153651435678125000*pi^3*cos((5*pi)/43) + 40235469128414080991250000*pi^2*sin((5*pi)/43) + 102003116029984338644329*pi^4*sin((5*pi)/43) - 779757153651435678125000*pi^3 + 1384100138017444386099000000*pi*cos((5*pi)/43)))/(40612351752678948837785600*pi^4) + (t*(53979905382680331057861000000*pi - 23806522373900043440902800000*sin((20*pi)/43) + 46254414597449512990696875000*pi^3*cos((20*pi)/43) + 61198148544317817187691250000*pi^2*sin((20*pi)/43) + 235978190751522998377675126089*pi^4*sin((20*pi)/43) - 46254414597449512990696875000*pi^3 - 53979905382680331057861000000*pi*cos((20*pi)/43)))/(93954279651069340078235556249600*pi^4) + (t*(49827604968627997899564000000*pi - 23806522373900043440902800000*sin((8*pi)/43) - 36380349760761382998600000000*pi^3*cos((8*pi)/43) + 52145167990424648964660000000*pi^2*sin((8*pi)/43) + 171326065733818174936433297664*pi^4*sin((8*pi)/43) - 36380349760761382998600000000*pi^3 + 49827604968627997899564000000*pi*cos((8*pi)/43)))/(68213155801427605331126098329600*pi^4) + (t*(29066102898366332108079000000*pi - 23806522373900043440902800000*sin((19*pi)/43) - 7221330999965945815115625000*pi^3*cos((19*pi)/43) + 17743841885630609717141250000*pi^2*sin((19*pi)/43) + 19837668008627384163887748249*pi^4*sin((19*pi)/43) - 7221330999965945815115625000*pi^3 + 29066102898366332108079000000*pi*cos((19*pi)/43)))/(7898330781212754648921381273600*pi^4) + (t*(27682002760348887721980000000*pi - 23806522373900043440902800000*sin((14*pi)/43) - 6238057229211485425000000000*pi^3*cos((14*pi)/43) + 16094187651365632396500000000*pi^2*sin((14*pi)/43) + 16320498564797494183092640000*pi^4*sin((14*pi)/43) - 6238057229211485425000000000*pi^3 + 27682002760348887721980000000*pi*cos((14*pi)/43)))/(6497976280428631814045696000000*pi^4) + (t*(9688700966122110702693000000*pi - 23806522373900043440902800000*sin((8*pi)/43) + 267456703702442437596875000*pi^3*cos((8*pi)/43) + 1971537987292289968571250000*pi^2*sin((8*pi)/43) + 244909481587992397085033929*pi^4*sin((8*pi)/43) - 267456703702442437596875000*pi^3 - 9688700966122110702693000000*pi*cos((8*pi)/43)))/(97510256558182156159523225600*pi^4) + (t*(4152300414052333158297000000*pi - 23806522373900043440902800000*sin((15*pi)/43) - 21053443148588763309375000*pi^3*cos((15*pi)/43) + 362119222155726728921250000*pi^2*sin((15*pi)/43) + 8262252398428731430190649*pi^4*sin((15*pi)/43) - 21053443148588763309375000*pi^3 + 4152300414052333158297000000*pi*cos((15*pi)/43)))/(3289600491966994855860633600*pi^4) - (t*(2139653629619539500775000000*pi^3*cos((16*pi)/43) - 23806522373900043440902800000*sin((16*pi)/43) - 19377401932244221405386000000*pi + 7886151949169159874285000000*pi^2*sin((16*pi)/43) + 3918551705407878353360542864*pi^4*sin((16*pi)/43) + 2139653629619539500775000000*pi^3 - 19377401932244221405386000000*pi*cos((16*pi)/43)))/(1560164104930914498552371609600*pi^4) - (t*(30647575167116027893025000000*pi^3*cos((2*pi)/43) - 23806522373900043440902800000*sin((2*pi)/43) - 47059404692593109127366000000*pi + 46512202312446677625885000000*pi^2*sin((2*pi)/43) + 136310436063045151166608038544*pi^4*sin((2*pi)/43) + 30647575167116027893025000000*pi^3 - 47059404692593109127366000000*pi*cos((2*pi)/43)))/(54271747691767975774091057561600*pi^4) + (t*(52595805244662886671762000000*pi - 23806522373900043440902800000*sin((18*pi)/43) - 42786834535161578530075000000*pi^3*cos((18*pi)/43) + 58100017421429932951365000000*pi^2*sin((18*pi)/43) + 212690369346297423943481593744*pi^4*sin((18*pi)/43) - 42786834535161578530075000000*pi^3 + 52595805244662886671762000000*pi*cos((18*pi)/43)))/(84682276684173972663824914841600*pi^4) + (t*(26297902622331443335881000000*pi - 23806522373900043440902800000*sin((9*pi)/43) - 5348354316895197316259375000*pi^3*cos((9*pi)/43) + 14525004355357483237841250000*pi^2*sin((9*pi)/43) + 13293148084143588996467599609*pi^4*sin((9*pi)/43) - 5348354316895197316259375000*pi^3 + 26297902622331443335881000000*pi*cos((9*pi)/43)))/(5292642292760873291489057177600*pi^4) - (t*(28022132830771643964778125000*pi^3*cos((7*pi)/43) - 23806522373900043440902800000*sin((7*pi)/43) - 45675304554575664741267000000*pi + 43816425880842934199471250000*pi^2*sin((7*pi)/43) + 120967637365395056869421292009*pi^4*sin((7*pi)/43) + 28022132830771643964778125000*pi^3 - 45675304554575664741267000000*pi*cos((7*pi)/43)))/(48163040802888771684655536537600*pi^4) - (t*(31544607796676639497140000000*pi^2*sin((11*pi)/43) - 23806522373900043440902800000*sin((11*pi)/43) - 17117229036956316006200000000*pi^3*cos((11*pi)/43) - 38754803864488442810772000000*pi + 62696827286526053653768685824*pi^4*sin((11*pi)/43) + 17117229036956316006200000000*pi^3 + 38754803864488442810772000000*pi*cos((11*pi)/43)))/(24962625678894631976837945753600*pi^4) - (t*(86234903136619574515200000000*pi^3*cos((18*pi)/43) - 23806522373900043440902800000*sin((18*pi)/43) - 66436806624837330532752000000*pi + 92702520871866042603840000000*pi^2*sin((18*pi)/43) + 541474973183425343008974372864*pi^4*sin((18*pi)/43) + 86234903136619574515200000000*pi^3 - 66436806624837330532752000000*pi*cos((18*pi)/43)))/(215587257841548974873682483609600*pi^4) - (t*(23229745364429920287021875000*pi^3*cos((17*pi)/43) - 23806522373900043440902800000*sin((17*pi)/43) - 42907104278540775969069000000*pi + 38666285832405931832591250000*pi^2*sin((17*pi)/43) + 94202019719127166409149362409*pi^4*sin((17*pi)/43) + 23229745364429920287021875000*pi^3 - 42907104278540775969069000000*pi*cos((17*pi)/43)))/(37506359702985815509620595097600*pi^4) + (t*(24913802484313998949782000000*pi - 23806522373900043440902800000*sin((4*pi)/43) - 4547543720095172874825000000*pi^3*cos((4*pi)/43) + 13036291997606162241165000000*pi^2*sin((4*pi)/43) + 10707879108363635933527081104*pi^4*sin((4*pi)/43) - 4547543720095172874825000000*pi^3 + 24913802484313998949782000000*pi*cos((4*pi)/43)))/(4263322237589225333195381145600*pi^4) + (t*(48443504830610553513465000000*pi - 23806522373900043440902800000*sin((3*pi)/43) - 33432087962805304699609375000*pi^3*cos((3*pi)/43) + 49288449682307249214281250000*pi^2*sin((3*pi)/43) + 153068425992495248178146205625*pi^4*sin((3*pi)/43) - 33432087962805304699609375000*pi^3 + 48443504830610553513465000000*pi*cos((3*pi)/43)))/(60943910348863847599702016000000*pi^4) - (t*(2631680393573595413671875000*pi^3*cos((11*pi)/43) - 23806522373900043440902800000*sin((11*pi)/43) - 20761502070261665791485000000*pi + 9052980553893168223031250000*pi^2*sin((11*pi)/43) + 5163907749017957143869155625*pi^4*sin((11*pi)/43) + 2631680393573595413671875000*pi^3 - 20761502070261665791485000000*pi*cos((11*pi)/43)))/(2056000307479371784912896000000*pi^4) + (t*(5536400552069777544396000000*pi - 23806522373900043440902800000*sin((20*pi)/43) - 49904457833691883400000000*pi^3*cos((20*pi)/43) + 643767506054625295860000000*pi^2*sin((20*pi)/43) + 26112797703675990692948224*pi^4*sin((20*pi)/43) - 49904457833691883400000000*pi^3 + 5536400552069777544396000000*pi*cos((20*pi)/43)))/(10396762048685810902473113600*pi^4) - (t*(3193885301356280537600000000*pi^3*cos((6*pi)/43) - 23806522373900043440902800000*sin((6*pi)/43) - 22145602208279110177584000000*pi + 10300280096874004733760000000*pi^2*sin((6*pi)/43) + 6684876212141053617394745344*pi^4*sin((6*pi)/43) + 3193885301356280537600000000*pi^3 - 22145602208279110177584000000*pi*cos((6*pi)/43)))/(2661571084463567591033117081600*pi^4) - (t*(4868491764538103799941250000*pi^2*sin((12*pi)/43) - 23806522373900043440902800000*sin((12*pi)/43) - 1037856771510060887584375000*pi^3*cos((12*pi)/43) - 15225101518191888247089000000*pi + 1493427621795000702091620889*pi^4*sin((12*pi)/43) + 1037856771510060887584375000*pi^3 + 15225101518191888247089000000*pi*cos((12*pi)/43)))/(594605442010972489934018969600*pi^4) + (t*(55364005520697775443960000000*pi - 23806522373900043440902800000*sin((15*pi)/43) + 49904457833691883400000000000*pi^3*cos((15*pi)/43) + 64376750605462529586000000000*pi^2*sin((15*pi)/43) + 261127977036759906929482240000*pi^4*sin((15*pi)/43) - 49904457833691883400000000000*pi^3 - 55364005520697775443960000000*pi*cos((15*pi)/43)))/(103967620486858109024731136000000*pi^4) + (t*(33218403312418665266376000000*pi - 23806522373900043440902800000*sin((9*pi)/43) + 10779362892077446814400000000*pi^3*cos((9*pi)/43) + 23175630217966510650960000000*pi^2*sin((9*pi)/43) + 33842185823964083938060898304*pi^4*sin((9*pi)/43) - 10779362892077446814400000000*pi^3 - 33218403312418665266376000000*pi*cos((9*pi)/43)))/(13474203615096810929605155225600*pi^4) - (t*(5793907554491627662740000000*pi^2*sin((17*pi)/43) - 23806522373900043440902800000*sin((17*pi)/43) - 1347420361509680851800000000*pi^3*cos((17*pi)/43) - 16609201656209332633188000000*pi + 2115136613997755246128806144*pi^4*sin((17*pi)/43) + 1347420361509680851800000000*pi^3 + 16609201656209332633188000000*pi*cos((17*pi)/43)))/(842137725943550683100322201600*pi^4) - (t*(85138252675724195377485000000*pi^2*sin((15*pi)/43) - 23806522373900043440902800000*sin((15*pi)/43) - 75898442307816143165975000000*pi^3*cos((15*pi)/43) - 63668606348802441760554000000*pi + 456714463887149556969082747024*pi^4*sin((15*pi)/43) + 75898442307816143165975000000*pi^3 + 63668606348802441760554000000*pi*cos((15*pi)/43)))/(181840018029142875547436161433600*pi^4) - (t*(77895868232609660799060000000*pi^2*sin((5*pi)/43) - 23806522373900043440902800000*sin((5*pi)/43) - 66422833376643896805400000000*pi^3*cos((5*pi)/43) - 60900406072767552988356000000*pi + 382317471179520179735454947584*pi^4*sin((5*pi)/43) + 66422833376643896805400000000*pi^3 + 60900406072767552988356000000*pi*cos((5*pi)/43)))/(152218993154808957423108856217600*pi^4) - (t*(4023546912841408099125000000*pi^2*sin((7*pi)/43) - 23806522373900043440902800000*sin((7*pi)/43) - 779757153651435678125000000*pi^3*cos((7*pi)/43) - 13841001380174443860990000000*pi + 1020031160299843386443290000*pi^4*sin((7*pi)/43) + 779757153651435678125000000*pi^3 + 13841001380174443860990000000*pi*cos((7*pi)/43)))/(406123517526789488377856000000*pi^4) + (t*(30450203036383776494178000000*pi - 23806522373900043440902800000*sin((19*pi)/43) + 8302854172080487100675000000*pi^3*cos((19*pi)/43) + 19473967058152415199765000000*pi^2*sin((19*pi)/43) + 23894841948720011233465934224*pi^4*sin((19*pi)/43) - 8302854172080487100675000000*pi^3 - 30450203036383776494178000000*pi*cos((19*pi)/43)))/(9513687072175559838944303513600*pi^4) - (t*(88880151304666704909671250000*pi^2*sin((20*pi)/43) - 23806522373900043440902800000*sin((20*pi)/43) - 80956726963553006409971875000*pi^3*cos((20*pi)/43) - 65052706486819886146653000000*pi + 497742667232310007580297979049*pi^4*sin((20*pi)/43) + 80956726963553006409971875000*pi^3 + 65052706486819886146653000000*pi*cos((20*pi)/43)))/(198175321212864165743714474393600*pi^4) + (t*(2768200276034888772198000000*pi - 23806522373900043440902800000*sin((10*pi)/43) - 6238057229211485425000000*pi^3*cos((10*pi)/43) + 160941876513656323965000000*pi^2*sin((10*pi)/43) + 1632049856479749418309264*pi^4*sin((10*pi)/43) - 6238057229211485425000000*pi^3 + 2768200276034888772198000000*pi*cos((10*pi)/43)))/(649797628042863181404569600*pi^4) - (t*(3259072999401540560291250000*pi^2*sin((2*pi)/43) - 23806522373900043440902800000*sin((2*pi)/43) - 568442965011896609353125000*pi^3*cos((2*pi)/43) - 12456901242156999474891000000*pi + 669242444272727245845442569*pi^4*sin((2*pi)/43) + 568442965011896609353125000*pi^3 + 12456901242156999474891000000*pi*cos((2*pi)/43)))/(266457639849326583324711321600*pi^4) + (t*(11072801104139555088792000000*pi - 23806522373900043440902800000*sin((3*pi)/43) + 399235662669535067200000000*pi^3*cos((3*pi)/43) + 2575070024218501183440000000*pi^2*sin((3*pi)/43) + 417804763258815851087171584*pi^4*sin((3*pi)/43) - 399235662669535067200000000*pi^3 - 11072801104139555088792000000*pi*cos((3*pi)/43)))/(166348192778972974439569817600*pi^4) + (t*(31834303174401220880277000000*pi - 23806522373900043440902800000*sin((14*pi)/43) + 9487305288477017895746875000*pi^3*cos((14*pi)/43) + 21284563168931048844371250000*pi^2*sin((14*pi)/43) + 28544653992946847310567671689*pi^4*sin((14*pi)/43) - 9487305288477017895746875000*pi^3 - 31834303174401220880277000000*pi*cos((14*pi)/43)))/(11365001126821429721714760089600*pi^4) - (t*(1713126466572204184840625000*pi^3*cos((21*pi)/43) - 23806522373900043440902800000*sin((21*pi)/43) - 17993301794226777019287000000*pi + 6799794282701979687521250000*pi^2*sin((21*pi)/43) + 2913310996932382696020680569*pi^4*sin((21*pi)/43) + 1713126466572204184840625000*pi^3 - 17993301794226777019287000000*pi*cos((21*pi)/43)))/(1159929378408263457755994521600*pi^4) - (t*(25551082410850244300800000000*pi^3*cos((12*pi)/43) - 23806522373900043440902800000*sin((12*pi)/43) - 44291204416558220355168000000*pi + 41201120387496018935040000000*pi^2*sin((12*pi)/43) + 106958019394256857878315925504*pi^4*sin((12*pi)/43) + 25551082410850244300800000000*pi^3 - 44291204416558220355168000000*pi*cos((12*pi)/43)))/(42585137351417081456529873305600*pi^4) - (t*(97469644206429459765625000000*pi^3*cos((8*pi)/43) - 23806522373900043440902800000*sin((8*pi)/43) - 69205006900872219304950000000*pi + 100588672821035202478125000000*pi^2*sin((8*pi)/43) + 637519475187402116527056250000*pi^4*sin((8*pi)/43) + 97469644206429459765625000000*pi^3 - 69205006900872219304950000000*pi*cos((8*pi)/43)))/(253827198454243430236160000000000*pi^4) + (t*(8304600828104666316594000000*pi - 23806522373900043440902800000*sin((13*pi)/43) + 168427545188710106475000000*pi^3*cos((13*pi)/43) + 1448476888622906915685000000*pi^2*sin((13*pi)/43) + 132196038374859702883050384*pi^4*sin((13*pi)/43) - 168427545188710106475000000*pi^3 - 8304600828104666316594000000*pi*cos((13*pi)/43)))/(52633607871471917693770137600*pi^4)
 
 
f3a =
 
(929942280230470446910265625*sin((5*pi*n)/43))/(147573952589676412928*n^4*pi^4) - (4191194700876466769921875*sin((5*pi*n)/43))/(1180591620717411303424*n^2*pi^2) + (4386133989289326561706147*sin((5*pi*n)/86)^2)/(4722366482869645213696*n*pi) + (108132823282612842663984375*sin((5*pi*n)/86)^2)/(295147905179352825856*n^3*pi^3) - (7997503609982045843428284375*sin((5*pi*n)/86)^2)/(36893488147419103232*n^5*pi^5)
 
 
f3 =
 
(33*t*pi*((161106849927982578125*sin((7*pi)/43))/(21250649172913403461632*pi^2) - (1083223874606690134375*sin((7*pi)/43))/(87658927838267789279232*pi^4) + (102003116029984338644329*sin((7*pi)/86)^2)/(1558380939346982920519680*pi) + (125956264489150015625*sin((7*pi)/86)^2)/(5312662293228350865408*pi^3) - (9315725321617535155625*sin((7*pi)/86)^2)/(723186154665709261553664*pi^5)))/430 + (22*t*pi*((161106849927982578125*sin((5*pi)/43))/(37778931862957161709568*pi^2) - (3249671623820070403125*sin((5*pi)/43))/(831136500985057557610496*pi^4) + (102003116029984338644329*sin((19*pi)/43)^2)/(2077841252462643894026240*pi) + (377868793467450046875*sin((19*pi)/43)^2)/(37778931862957161709568*pi^3) - (27947175964852605466875*sin((19*pi)/43)^2)/(9142501510835633133715456*pi^5)))/215 + (11*t*pi*((3249671623820070403125*sin((19*pi)/43))/(51946031311566097350656*pi^4) - (161106849927982578125*sin((19*pi)/43))/(9444732965739290427392*pi^2) + (102003116029984338644329*sin((12*pi)/43)^2)/(1038920626231321947013120*pi) + (377868793467450046875*sin((12*pi)/43)^2)/(4722366482869645213696*pi^3) - (27947175964852605466875*sin((12*pi)/43)^2)/(285703172213613535428608*pi^5)))/215 + (11*t*pi*((161106849927982578125*sin((12*pi)/43))/(2361183241434822606848*pi^2) - (3249671623820070403125*sin((12*pi)/43))/(3246626956972881084416*pi^4) + (102003116029984338644329*sin((31*pi)/86)^2)/(519460313115660973506560*pi) + (377868793467450046875*sin((31*pi)/86)^2)/(590295810358705651712*pi^3) - (27947175964852605466875*sin((31*pi)/86)^2)/(8928224131675422982144*pi^5)))/430 + (17*t*pi*((19493928841285891953125*sin((2*pi)/43))/(2729527827098654933516288*pi^2) - (4325312931304513706559375*sin((2*pi)/43))/(394416771015755637893103616*pi^4) + (102003116029984338644329*sin(pi/43)^2)/(1605604604175679372656640*pi) + (502943364105176012390625*sin(pi/43)^2)/(23200986530338566934888448*pi^3) - (37197691209218817876410625*sin(pi/43)^2)/(3352542553633922922091380736*pi^5)))/215 + (8*t*pi*((19493928841285891953125*sin((6*pi)/43))/(604462909807314587353088*pi^2) - (4325312931304513706559375*sin((6*pi)/43))/(19342813113834066795298816*pi^4) + (102003116029984338644329*sin((3*pi)/43)^2)/(755578637259143234191360*pi) + (502943364105176012390625*sin((3*pi)/43)^2)/(2417851639229258349412352*pi^3) - (37197691209218817876410625*sin((3*pi)/43)^2)/(77371252455336267181195264*pi^5)))/215 + (t*pi*((4325312931304513706559375*sin((10*pi)/43))/(4722366482869645213696*pi^4) - (19493928841285891953125*sin((10*pi)/43))/(9444732965739290427392*pi^2) + (102003116029984338644329*sin((5*pi)/43)^2)/(94447329657392904273920*pi) + (502943364105176012390625*sin((5*pi)/43)^2)/(4722366482869645213696*pi^3) - (37197691209218817876410625*sin((5*pi)/43)^2)/(2361183241434822606848*pi^5)))/215 + (16*t*pi*((19493928841285891953125*sin((12*pi)/43))/(2417851639229258349412352*pi^2) - (4325312931304513706559375*sin((12*pi)/43))/(309485009821345068724781056*pi^4) + (102003116029984338644329*sin((6*pi)/43)^2)/(1511157274518286468382720*pi) + (502943364105176012390625*sin((6*pi)/43)^2)/(19342813113834066795298816*pi^3) - (37197691209218817876410625*sin((6*pi)/43)^2)/(2475880078570760549798248448*pi^5)))/215 + (7*t*pi*((19493928841285891953125*sin((16*pi)/43))/(462791915321225230942208*pi^2) - (4325312931304513706559375*sin((16*pi)/43))/(11338401925370018158084096*pi^4) + (102003116029984338644329*sin((8*pi)/43)^2)/(661131307601750329917440*pi) + (502943364105176012390625*sin((8*pi)/43)^2)/(1619771703624288308297728*pi^3) - (37197691209218817876410625*sin((8*pi)/43)^2)/(39684406738795063553294336*pi^5)))/215 + (19*t*pi*((4325312931304513706559375*sin((18*pi)/43))/(615423522414055033894076416*pi^4) - (19493928841285891953125*sin((18*pi)/43))/(3409548600631883844288512*pi^2) + (102003116029984338644329*sin((9*pi)/43)^2)/(1794499263490465181204480*pi) + (502943364105176012390625*sin((9*pi)/43)^2)/(32390711706002896520740864*pi^3) - (37197691209218817876410625*sin((9*pi)/43)^2)/(5846523462933522821993725952*pi^5)))/215 + (13*t*pi*((19493928841285891953125*sin(pi/43))/(1596159871209940082229248*pi^2) - (4325312931304513706559375*sin(pi/43))/(134875509117239936948371456*pi^4) + (102003116029984338644329*sin((21*pi)/43)^2)/(1227815285546107755560960*pi) + (502943364105176012390625*sin((21*pi)/43)^2)/(10375039162864610534490112*pi^3) - (37197691209218817876410625*sin((21*pi)/43)^2)/(876690809262059590164414464*pi^5)))/215 + (4*t*pi*((4325312931304513706559375*sin((3*pi)/43))/(1208925819614629174706176*pi^4) - (19493928841285891953125*sin((3*pi)/43))/(151115727451828646838272*pi^2) + (102003116029984338644329*sin((20*pi)/43)^2)/(377789318629571617095680*pi) + (502943364105176012390625*sin((20*pi)/43)^2)/(302231454903657293676544*pi^3) - (37197691209218817876410625*sin((20*pi)/43)^2)/(2417851639229258349412352*pi^5)))/215 + (14*t*pi*((19493928841285891953125*sin((11*pi)/43))/(1851167661284900923768832*pi^2) - (4325312931304513706559375*sin((11*pi)/43))/(181414430805920290529345536*pi^4) + (102003116029984338644329*sin((16*pi)/43)^2)/(1322262615203500659834880*pi) + (502943364105176012390625*sin((16*pi)/43)^2)/(12958173628994306466381824*pi^3) - (37197691209218817876410625*sin((16*pi)/43)^2)/(1269901015641442033705418752*pi^5)))/215 + (2*t*pi*((4325312931304513706559375*sin((20*pi)/43))/(75557863725914323419136*pi^4) - (19493928841285891953125*sin((20*pi)/43))/(37778931862957161709568*pi^2) + (102003116029984338644329*sin((10*pi)/43)^2)/(188894659314785808547840*pi) + (502943364105176012390625*sin((10*pi)/43)^2)/(37778931862957161709568*pi^3) - (37197691209218817876410625*sin((10*pi)/43)^2)/(75557863725914323419136*pi^5)))/215 + (23*t*pi*((19493928841285891953125*sin((15*pi)/43))/(4996263738876084636090368*pi^2) - (4325312931304513706559375*sin((15*pi)/43))/(1321511758932724386245902336*pi^4) + (102003116029984338644329*sin((14*pi)/43)^2)/(2172288582120036798300160*pi) + (502943364105176012390625*sin((14*pi)/43)^2)/(57457032997074973315039232*pi^3) - (37197691209218817876410625*sin((14*pi)/43)^2)/(15197385227726330441827876864*pi^5)))/215 + (17*t*pi*((19493928841285891953125*sin(pi/43))/(682381956774663733379072*pi^2) - (4325312931304513706559375*sin(pi/43))/(24651048188484727368318976*pi^4) + (102003116029984338644329*sin(pi/86)^2)/(802802302087839686328320*pi) + (502943364105176012390625*sin(pi/86)^2)/(2900123316292320866861056*pi^3) - (37197691209218817876410625*sin(pi/86)^2)/(104766954801060091315355648*pi^5)))/430 + (t*pi*((4325312931304513706559375*sin((5*pi)/43))/(295147905179352825856*pi^4) - (19493928841285891953125*sin((5*pi)/43))/(2361183241434822606848*pi^2) + (102003116029984338644329*sin((5*pi)/86)^2)/(47223664828696452136960*pi) + (502943364105176012390625*sin((5*pi)/86)^2)/(590295810358705651712*pi^3) - (37197691209218817876410625*sin((5*pi)/86)^2)/(73786976294838206464*pi^5)))/430 + (19*t*pi*((4325312931304513706559375*sin((9*pi)/43))/(38463970150878439618379776*pi^4) - (19493928841285891953125*sin((9*pi)/43))/(852387150157970961072128*pi^2) + (102003116029984338644329*sin((9*pi)/86)^2)/(897249631745232590602240*pi) + (502943364105176012390625*sin((9*pi)/86)^2)/(4048838963250362065092608*pi^3) - (37197691209218817876410625*sin((9*pi)/86)^2)/(182703858216672588187303936*pi^5)))/430 + (37*t*pi*((4325312931304513706559375*sin((13*pi)/43))/(553154693118841071459106816*pi^4) - (19493928841285891953125*sin((13*pi)/43))/(3232459857524272148774912*pi^2) + (102003116029984338644329*sin((13*pi)/86)^2)/(1747275598661768729067520*pi) + (502943364105176012390625*sin((13*pi)/86)^2)/(29900253682099517376167936*pi^3) - (37197691209218817876410625*sin((13*pi)/86)^2)/(5116680911349279910996738048*pi^5)))/430 + (49*t*pi*((19493928841285891953125*sin((13*pi)/43))/(5669200962685009079042048*pi^2) - (4325312931304513706559375*sin((13*pi)/43))/(1701468938925838349847494656*pi^4) + (102003116029984338644329*sin((13*pi)/86)^2)/(2313959576606126154711040*pi) + (502943364105176012390625*sin((13*pi)/86)^2)/(69447711792891361218265088*pi^3) - (37197691209218817876410625*sin((13*pi)/86)^2)/(20842994501841519785631809536*pi^5)))/430 + (31*t*pi*((19493928841285891953125*sin((17*pi)/43))/(2269097095018864525180928*pi^2) - (4325312931304513706559375*sin((17*pi)/43))/(272575288539141101087358976*pi^4) + (102003116029984338644329*sin((17*pi)/86)^2)/(1463933609689590016245760*pi) + (502943364105176012390625*sin((17*pi)/86)^2)/(17585502486396200070152192*pi^3) - (37197691209218817876410625*sin((17*pi)/86)^2)/(2112458486178343533427032064*pi^5)))/430 + (13*t*pi*((19493928841285891953125*sin((21*pi)/43))/(399039967802485020557312*pi^2) - (4325312931304513706559375*sin((21*pi)/43))/(8429719319827496059273216*pi^4) + (102003116029984338644329*sin((21*pi)/86)^2)/(613907642773053877780480*pi) + (502943364105176012390625*sin((21*pi)/86)^2)/(1296879895358076316811264*pi^3) - (37197691209218817876410625*sin((21*pi)/86)^2)/(27396587789439362192637952*pi^5)))/430 + (47*t*pi*((19493928841285891953125*sin((20*pi)/43))/(5215853780329523138527232*pi^2) - (4325312931304513706559375*sin((20*pi)/43))/(1440227625093489576625831936*pi^4) + (102003116029984338644329*sin((23*pi)/86)^2)/(2219512246948733250437120*pi) + (502943364105176012390625*sin((23*pi)/86)^2)/(61286281918871896877694976*pi^3) - (37197691209218817876410625*sin((23*pi)/86)^2)/(16922674594848502525353525248*pi^5)))/430 + (29*t*pi*((19493928841285891953125*sin((16*pi)/43))/(1985755106046685812359168*pi^2) - (4325312931304513706559375*sin((16*pi)/43))/(208752505523157846024257536*pi^4) + (102003116029984338644329*sin((27*pi)/86)^2)/(1369486280032197111971840*pi) + (502943364105176012390625*sin((27*pi)/86)^2)/(14396724518838472139603968*pi^3) - (37197691209218817876410625*sin((27*pi)/86)^2)/(1513455665042894383675867136*pi^5)))/430 + (23*t*pi*((4325312931304513706559375*sin((14*pi)/43))/(82594484933295274140368896*pi^4) - (19493928841285891953125*sin((14*pi)/43))/(1249065934719021159022592*pi^2) + (102003116029984338644329*sin((29*pi)/86)^2)/(1086144291060018399150080*pi) + (502943364105176012390625*sin((29*pi)/86)^2)/(7182129124634371664379904*pi^3) - (37197691209218817876410625*sin((29*pi)/86)^2)/(474918288366447826307121152*pi^5)))/430 + (41*t*pi*((4325312931304513706559375*sin((10*pi)/43))/(834017439687513220543676416*pi^4) - (19493928841285891953125*sin((10*pi)/43))/(3969149028851936802111488*pi^2) + (102003116029984338644329*sin((33*pi)/86)^2)/(1936170257976554537615360*pi) + (502943364105176012390625*sin((33*pi)/86)^2)/(40683777545732352221642752*pi^3) - (37197691209218817876410625*sin((33*pi)/86)^2)/(8548678756797010510572683264*pi^5)))/430 + (7*t*pi*((4325312931304513706559375*sin((8*pi)/43))/(708650120335626134880256*pi^4) - (19493928841285891953125*sin((8*pi)/43))/(115697978830306307735552*pi^2) + (102003116029984338644329*sin((35*pi)/86)^2)/(330565653800875164958720*pi) + (502943364105176012390625*sin((35*pi)/86)^2)/(202471462953036038537216*pi^3) - (37197691209218817876410625*sin((35*pi)/86)^2)/(1240137710587345736040448*pi^5)))/430 + (9*t*pi*((1441770977101504568853125*sin((4*pi)/43))/(10327815498035914082353152*pi^4) - (19493928841285891953125*sin((4*pi)/43))/(765023370224882524618752*pi^2) + (102003116029984338644329*sin((2*pi)/43)^2)/(850025966916536138465280*pi) + (167647788035058670796875*sin((2*pi)/43)^2)/(1147535055337323786928128*pi^3) - (12399230403072939292136875*sin((2*pi)/43)^2)/(46475169741161613370589184*pi^5)))/215 + (18*t*pi*((1441770977101504568853125*sin((8*pi)/43))/(165245047968574625317650432*pi^4) - (19493928841285891953125*sin((8*pi)/43))/(3060093480899530098475008*pi^2) + (102003116029984338644329*sin((4*pi)/43)^2)/(1700051933833072276930560*pi) + (167647788035058670796875*sin((4*pi)/43)^2)/(9180280442698590295425024*pi^3) - (12399230403072939292136875*sin((4*pi)/43)^2)/(1487205431717171627858853888*pi^5)))/215 + (24*t*pi*((19493928841285891953125*sin((18*pi)/43))/(5440166188265831286177792*pi^2) - (1441770977101504568853125*sin((18*pi)/43))/(522255954073519803473068032*pi^4) + (102003116029984338644329*sin((9*pi)/43)^2)/(2266735911777429702574080*pi) + (167647788035058670796875*sin((9*pi)/43)^2)/(21760664753063325144711168*pi^3) - (12399230403072939292136875*sin((9*pi)/43)^2)/(6267071448882237641676816384*pi^5)))/215 + (21*t*pi*((1441770977101504568853125*sin((5*pi)/43))/(306136851984990490268270592*pi^4) - (19493928841285891953125*sin((5*pi)/43))/(4165127237891027078479872*pi^2) + (102003116029984338644329*sin((19*pi)/43)^2)/(1983393922805250989752320*pi) + (167647788035058670796875*sin((19*pi)/43)^2)/(14577945332618594774679552*pi^3) - (12399230403072939292136875*sin((19*pi)/43)^2)/(3214436945842400147816841216*pi^5)))/215 + (12*t*pi*((1441770977101504568853125*sin((9*pi)/43))/(32640997129594987717066752*pi^4) - (19493928841285891953125*sin((9*pi)/43))/(1360041547066457821544448*pi^2) + (102003116029984338644329*sin((17*pi)/43)^2)/(1133367955888714851287040*pi) + (167647788035058670796875*sin((17*pi)/43)^2)/(2720083094132915643088896*pi^3) - (12399230403072939292136875*sin((17*pi)/43)^2)/(195845982777569926302400512*pi^5)))/215 + (3*t*pi*((1441770977101504568853125*sin((13*pi)/43))/(127503895037480420769792*pi^4) - (19493928841285891953125*sin((13*pi)/43))/(85002596691653613846528*pi^2) + (102003116029984338644329*sin((15*pi)/43)^2)/(283341988972178712821760*pi) + (167647788035058670796875*sin((15*pi)/43)^2)/(42501298345826806923264*pi^3) - (12399230403072939292136875*sin((15*pi)/43)^2)/(191255842556220631154688*pi^5)))/215 + (6*t*pi*((19493928841285891953125*sin((17*pi)/43))/(340010386766614455386112*pi^2) - (1441770977101504568853125*sin((17*pi)/43))/(2040062320599686732316672*pi^4) + (102003116029984338644329*sin((13*pi)/43)^2)/(566683977944357425643520*pi) + (167647788035058670796875*sin((13*pi)/43)^2)/(340010386766614455386112*pi^3) - (12399230403072939292136875*sin((13*pi)/43)^2)/(6120186961799060196950016*pi^5)))/215 + (3*t*pi*((1441770977101504568853125*sin((15*pi)/43))/(7968993439842526298112*pi^4) - (19493928841285891953125*sin((15*pi)/43))/(21250649172913403461632*pi^2) + (102003116029984338644329*sin((15*pi)/86)^2)/(141670994486089356410880*pi) + (167647788035058670796875*sin((15*pi)/86)^2)/(5312662293228350865408*pi^3) - (12399230403072939292136875*sin((15*pi)/86)^2)/(5976745079881894723584*pi^5)))/430 + (21*t*pi*((1441770977101504568853125*sin((19*pi)/43))/(19133553249061905641766912*pi^4) - (19493928841285891953125*sin((19*pi)/43))/(1041281809472756769619968*pi^2) + (102003116029984338644329*sin((19*pi)/86)^2)/(991696961402625494876160*pi) + (167647788035058670796875*sin((19*pi)/86)^2)/(1822243166577324346834944*pi^3) - (12399230403072939292136875*sin((19*pi)/86)^2)/(100451154557575004619276288*pi^5)))/430 + (39*t*pi*((1441770977101504568853125*sin((20*pi)/43))/(227602421635342393600376832*pi^4) - (19493928841285891953125*sin((20*pi)/43))/(3591359710222365185015808*pi^2) + (102003116029984338644329*sin((23*pi)/86)^2)/(1841722928319161633341440*pi) + (167647788035058670796875*sin((23*pi)/86)^2)/(11671919058222686851301376*pi^3) - (12399230403072939292136875*sin((23*pi)/86)^2)/(2219123610944588337603674112*pi^5)))/430 + (27*t*pi*((19493928841285891953125*sin((6*pi)/43))/(1721302583005985680392192*pi^2) - (1441770977101504568853125*sin((6*pi)/43))/(52284565958806815041912832*pi^4) + (102003116029984338644329*sin((37*pi)/86)^2)/(1275038950374804207697920*pi) + (167647788035058670796875*sin((37*pi)/86)^2)/(3872930811763467780882432*pi^3) - (12399230403072939292136875*sin((37*pi)/86)^2)/(352920820221946001532911616*pi^5)))/430 + (9*t*pi*((19493928841285891953125*sin((2*pi)/43))/(191255842556220631154688*pi^2) - (1441770977101504568853125*sin((2*pi)/43))/(645488468627244630147072*pi^4) + (102003116029984338644329*sin((41*pi)/86)^2)/(425012983458268069232640*pi) + (167647788035058670796875*sin((41*pi)/86)^2)/(143441881917165473366016*pi^3) - (12399230403072939292136875*sin((41*pi)/86)^2)/(1452349054411300417830912*pi^5)))/430 + (2*t*pi*((6920500690087221930495*sin((14*pi)/43))/(75557863725914323419136*pi^4) - (779757153651435678125*sin((14*pi)/43))/(37778931862957161709568*pi^2) + (102003116029984338644329*sin((7*pi)/43)^2)/(944473296573929042739200*pi) + (4023546912841408099125*sin((7*pi)/43)^2)/(37778931862957161709568*pi^3) - (59516305934750108602257*sin((7*pi)/43)^2)/(377789318629571617095680*pi^5)))/43 + (t*pi*((779757153651435678125*sin((7*pi)/43))/(9444732965739290427392*pi^2) - (6920500690087221930495*sin((7*pi)/43))/(4722366482869645213696*pi^4) + (102003116029984338644329*sin((18*pi)/43)^2)/(472236648286964521369600*pi) + (4023546912841408099125*sin((18*pi)/43)^2)/(4722366482869645213696*pi^3) - (59516305934750108602257*sin((18*pi)/43)^2)/(11805916207174113034240*pi^5)))/43 + (4*t*pi*((6920500690087221930495*sin((15*pi)/43))/(1208925819614629174706176*pi^4) - (779757153651435678125*sin((15*pi)/43))/(151115727451828646838272*pi^2) + (102003116029984338644329*sin((14*pi)/43)^2)/(1888946593147858085478400*pi) + (4023546912841408099125*sin((14*pi)/43)^2)/(302231454903657293676544*pi^3) - (59516305934750108602257*sin((14*pi)/43)^2)/(12089258196146291747061760*pi^5)))/43 + (7*t*pi*((6920500690087221930495*sin((3*pi)/43))/(708650120335626134880256*pi^4) - (779757153651435678125*sin((3*pi)/43))/(115697978830306307735552*pi^2) + (102003116029984338644329*sin((3*pi)/86)^2)/(1652828269004375824793600*pi) + (4023546912841408099125*sin((3*pi)/86)^2)/(202471462953036038537216*pi^3) - (59516305934750108602257*sin((3*pi)/86)^2)/(6200688552936728680202240*pi^5)))/86 + (t*pi*((6920500690087221930495*sin((18*pi)/43))/(295147905179352825856*pi^4) - (779757153651435678125*sin((18*pi)/43))/(2361183241434822606848*pi^2) + (102003116029984338644329*sin((25*pi)/86)^2)/(236118324143482260684800*pi) + (4023546912841408099125*sin((25*pi)/86)^2)/(590295810358705651712*pi^3) - (59516305934750108602257*sin((25*pi)/86)^2)/(368934881474191032320*pi^5)))/86 + (3*t*pi*((779757153651435678125*sin((21*pi)/43))/(85002596691653613846528*pi^2) - (2306833563362407310165*sin((21*pi)/43))/(127503895037480420769792*pi^4) + (102003116029984338644329*sin((11*pi)/43)^2)/(1416709944860893564108800*pi) + (1341182304280469366375*sin((11*pi)/43)^2)/(42501298345826806923264*pi^3) - (19838768644916702867419*sin((11*pi)/43)^2)/(956279212781103155773440*pi^5)))/43 + (3*t*pi*((779757153651435678125*sin((11*pi)/43))/(21250649172913403461632*pi^2) - (2306833563362407310165*sin((11*pi)/43))/(7968993439842526298112*pi^4) + (102003116029984338644329*sin((11*pi)/86)^2)/(708354972430446782054400*pi) + (1341182304280469366375*sin((11*pi)/86)^2)/(5312662293228350865408*pi^3) - (19838768644916702867419*sin((11*pi)/86)^2)/(29883725399409473617920*pi^5)))/86 + (9*t*pi*((779757153651435678125*sin((10*pi)/43))/(191255842556220631154688*pi^2) - (2306833563362407310165*sin((10*pi)/43))/(645488468627244630147072*pi^4) + (102003116029984338644329*sin((33*pi)/86)^2)/(2125064917291340346163200*pi) + (1341182304280469366375*sin((33*pi)/86)^2)/(143441881917165473366016*pi^3) - (19838768644916702867419*sin((33*pi)/86)^2)/(7261745272056502089154560*pi^5)))/86 + (t*pi*(102003116029984338644329/(2030617587633947441889280*pi) + 272008309413291515625/(25382719845424343023616*pi^3) - 10880332376531660625/(3172839980678042877952*pi^5)))/10 + (5*t*pi*((31190286146057427125*sin((8*pi)/43))/(9444732965739290427392*pi^2) - (1384100138017444386099*sin((8*pi)/43))/(590295810358705651712000*pi^4) + (102003116029984338644329*sin((4*pi)/43)^2)/(2361183241434822606848000*pi) + (32188375302731264793*sin((4*pi)/43)^2)/(4722366482869645213696*pi^3) - (59516305934750108602257*sin((4*pi)/43)^2)/(36893488147419103232000000*pi^5)))/43 + (5*t*pi*((1384100138017444386099*sin((4*pi)/43))/(36893488147419103232000*pi^4) - (31190286146057427125*sin((4*pi)/43))/(2361183241434822606848*pi^2) + (102003116029984338644329*sin((39*pi)/86)^2)/(1180591620717411303424000*pi) + (32188375302731264793*sin((39*pi)/86)^2)/(590295810358705651712*pi^3) - (59516305934750108602257*sin((39*pi)/86)^2)/(1152921504606846976000000*pi^5)))/86
 
Error using  ^  (line 51)
Incorrect dimensions for raising a matrix to a power. Check that the matrix is square and the power is a scalar.
To perform elementwise matrix powers, use '.^'.

I'm not sure how I should go about solving this and hope that some of you may be able to help me with this issue.

Thank you very much.

t = 0:10:1000;
y = f
plot(t,y)

[Walter Roberson]

Which MATLAB release are you using? The code works fine for me until the plot(t,y) which needs to be changed to

plot(t, subs(y))

Answer 1

[Star Strider]

I do not understand this:

Q = @(v) sym(v);        %convert to rational

However this runs without error:

syms n t v 
Q(v) = v;        %convert to rational
Pi = sym('pi');
f1 = Q(0.111627907);
f2a = int((Q(-0.3072*10^(-6))*(t - 25)^4 + Q(1.2))*cos((2*n*Pi*t)/860), t, 0, 50)
f2 = symsum(1/430*f2a*n*Pi*t/430, n, 1, 50)
f3a = int((Q(-0.3072*10^(-6))*(t - 25)^4 + Q(1.2))*sin((2*n*Pi*t)/860), t, 0, 50)
f3 = symsum(1/430*f3a*n*Pi*t/430, n, 1, 50)
f(t) = vpa(f1 + f2 + f3);
f=f+860  %causes the function to repeat for a period of 860

fplot(f, [0 1000])
grid
xlabel('t')
ylabel('f(t)')

[Taosui Li]

Thank you very much.

The code does run with error:

Error using sym/subsindex (line 845)
Invalid indexing or function definition. Indexing must follow MATLAB indexing. Function arguments must be
symbolic variables, and function body must be sym expression.

Line 845:

error(message('symbolic:sym:subscript:InvalidIndexOrFunction'));

What does this mean?

It is possible that tis is the result of the lack of some packages?

[Walter Roberson]

Q = @(v) sym(v); 

sym() applied to a floating point number is equivalent to sym(TheNumber, 'r') which approximates the number as a symbolic rational (or as a multiple of pi, or as a sqrt())

https://www.mathworks.com/help/symbolic/sym.html#bun735q-num

Using floating point numbers with the symbolic toolbox without converting to indefinite precision is a mistake more often than not (but not always)

[Star Strider]

@Taosui Li —

My pleasure.

Do not use the anonymous function with symbolic variables.

Use this instead, as I did in my code:

Q(v) = v;        %convert to rational

Then it will run without error.

[Walter Roberson]

Anonymous functions have their place with symbolic expressions -- especially when the argument to the anonymous function is non-symbolic.

Q(v) = v

is the same as

Q = symfun(v, v)

and results in an implicit conversion of numeric values to floating point, with no explicit control over how the conversion is done.

sym(v)

on the other hand is documented as converting using a default of 'r', and can easily be changed to (e.g.)

Q = @(v) sym(v,'d')

or 'e' or 'f' depending on how one wants the conversion to be done.

It is not a problem to have an anonymous function that returns a symbolic result.

[Star Strider]

Agreed that anonymous functions can be used with symbolic variables, however here it just seems to crash the code. Using a symbolic function and fplot avoids the crash.

[Walter Roberson]

Again I have to ask which release, as the original code works for me in the releases I have tested, except for the plot() call.

[Taosui Li]

Thank you very much,

After changing to this,

Q = symfun(v, v)

a graph is generated.

However, I did not expect a linear plot.

Perhaps there are some errors in my equation or code.

[Star Strider]

My pleasure.

The int function will by definition return a scalar. If you want a vector with perhaps varying upper levels of integration, this is best done numerically (rather than symbolically), possibly using the cumtrapz function, or the integral function with a loop. Anoather option is of course creating your integrand as a differential equation, and solving it as a function of ‘t’. I am not certain what you are doing, so I am simply presenting alternatives.

[Taosui Li]

Thank you very much.

I will try this.

[Star Strider]

My pleasure.

[Taosui Li]

Matlab returns 0 for functions that have int replaced by cumtrapz.

I do not know how to use integral as I cannot do function handles.

[Walter Roberson]

Is an assignment restriction forbiding you to use function handles? Or you just do not know how to use function handles?

Which MATLAB release are you using?

f=f+860  %causes the function to repeat for a period of 860

I cannot think of any mathematical function that is such that adding 860 to it would cause it to have a period of 860 ?

Your f that has not had that 860 added is linear, of the form constant*t + constant

[Star Strider]

Experiment with this:

Q = @(v) v;        %convert to rational
Pi = pi;
f1 = Q(0.111627907);
f2a = @(n) integral( @(t) (Q(-0.3072*10^(-6)).*(t - 25).^4 + Q(1.2))*cos((2*n.*Pi.*t)/860), 0, 50, 'ArrayValued',1);
f2 = @(n,t) cumsum(1/430*f2a(n).*n*Pi.*t/430);
f3a = @(n) integral(@(t)(Q(-0.3072*10^(-6))*(t - 25).^4 + Q(1.2))*sin((2*n.*Pi.*t)/860), 0, 50, 'ArrayValued',1);
f3 = @(n,t) cumsum(1/430*f3a(n).*n.*Pi.*t/430);
f = @(n,t) (f1 + f2(n,t) + f3(n,t));
f = @(n,t) f(n,t)+860  %causes the function to repeat for a period of 860
[N,T] = ndgrid(1:50, 0:10:1000);

figure
meshc(N, T, f(N,T))
grid on
xlabel('n')
ylabel('t')
zlabel('f(t)')

producing:

I changed your code only to be certain it works with integral and cumsum, including vectorising it and creating the ‘N’ and ‘T’ matrices.

I have no idea what your code is doing or what the output is supposed to look like, so I will let you take it from here now that it is running. Replacing cumsum with sum produces a straight line for all ‘t’, (it does not seem to vary with time although it does with ‘n’), so apparently cumsum is necessary.

With respect to programming with anonymous functions, see the documentation section on Anonymous Functions. For the other functions I use here and their name-value pair agruments, see their documentation pages.

Have fun!