gamma function for N>100

Hi, everyone.

I have written a simple code by using a gamma function. when I choose N>98, the answer is Nan. What should I do to fix this problem?

 function sii = diagonals(n, al, alp, bet)
ssi = zeros(1,n+1);
for i = 1:n+1
    sii(i) = (2^(al+1)*(gamma(i-1+alp+1))*(gamma(i-1+bet+1)))/((2*(i-1)+al+1)*(factorial(i-1))^2);
end
end

[John D'Errico]

Is there a good reason why you have not just used gamma itself? Why would you write your own poor code to compute something that is computed well already for you? I'm not going to try to decrypt what you are doing based on undocumented, poorly written code. Perhaps you are trying to write your own incomplete gamma. Oops, also exists already, part of MATLAB.

[Ladan Avazpour]

I have done this after I found that the gamma function is not working for big number and I think it may work if I can add something to it. In addition, this is my first time using Matlab and I just learning.

Answer 1

[Walter Roberson]

If gammaln cannot be made to suit your purpose then you should use the symbolic toolbox or equivalent

[Ladan Avazpour]

Thank you. gamma(sym(X)) is working properly.(after double(x))

Answer 2

[John D'Errico]

No. You will not make it work for large values, when they exceed the limits of gamma itself. Your code is not better than what you will find inside gamma itself. Sorry, but NOT.

Instead, consider using the function gammaln, the natural log of the gamma function. In essentially all cases when gamma produces an overflow, gammaln will be the solution, by re-writing what you are doing to accommodate logs. Only consider exponentiating at the end.

gammaln(10000)
ans =
         82099.7174964424

Those big numbers are meaningless in a double precision context, because they would vastly overflow the dynamic range of a double precision number.

[Ladan Avazpour]

Thank you