Limits of using vpa

Hi,

I need to evaluate the gamma function in MATLAB for some very large values, and have so far been using 'vpa' to do this.

However, this now seems to be hitting a limit around gamma(1e8), as shown below.

Is it posible to extend this somehow to calculate gamma(1e8)?

Thank you!

gamma(vpa(1e7))
 
ans =
 
1.2024234005159034561401534879443e+65657052
 
>> gamma(vpa(1e8))
 
ans =
 
Inf

[David Goodmanson]

Hi John,

at some point it make a lot more sense to use the logarithm.

vpa(gammaln(1e100),100)

ans = 2.292585092994046058293551528706245869611598545401159566538932922285195947207408619737372157648583e+102

Answer 1

[Pratheek Punchathody]

Hi John

Logarithm of gamma function command avoids the underflow and overflow that may occur.

By using the command

y=gammaln(1e8); 

Output obtained is y= 1.7421e+09

If the number of digits that has to be displayed is known (say 25) then

By using the command

z= vpa(gammaln(1e8),25); 

Output obtained is z = 1742068066.103834867477417

Refer to the documentation on vpa(x,d) for more information. Here d must be greater than 1 and lesser than 2^29+1.