Fourier Series Integration in terms of Pi

Hello,

The following code is just to check my integration of a fourier series transform, but the output doesn't seem to be right for bn. It displays a large number at the end of the bn output.

syms t
syms n 'integer'
an = (1/pi)*(int(-1*cos(n*pi*t/pi),-pi,-pi/2)+int(0*cos(n*pi*t/pi), -pi/2, pi/2)+int(1*cos(n*pi*t/pi), pi/2, pi))
bn = (1/pi)*(int(-1*sin(n*pi*t/pi),-pi,-pi/2)+int(0*sin(n*pi*t/pi), -pi/2, pi/2)+int(1*sin(n*pi*t/pi), pi/2, pi))

pretty(an)
pretty(bn)

Answer 1

[VBBV]

Hi @Bob Gill, the value of bn can be computed as follows

syms t n 'integer'
an = (1/pi)*(int(-1*cos(n*pi*t/pi),-pi,-pi/2)+int(0*cos(n*pi*t/pi), -pi/2, pi/2)+int(-1*cos(n*pi*t/pi), pi/2, pi))

an = 

bn = (1/pi)*(int(-1*sin(n*pi*t/pi),-pi,-pi/2)+int(0*sin(n*pi*t/pi), -pi/2, pi/2)+int(-1*sin(n*pi*t/pi), pi/2, pi))

bn = 

0

vpa(an,2)

ans = 

vpa(bn,2)

ans = 

0.0

[VBBV]

Use vpa to ccompute the bn value. You can also consider the vpaintegral function to compute the values for an and bn