Regularized hypergeometric function 1F2 within matlab?

Hi, I'm trying to find the special function to use within my code:

function [result] = sin_derivatve(x,n)
    if (rem(n,1) == 0) && (n ~= 0)
        result = sin(x+n*pi()/2);
    else
        part1 = 2.^(n-1).*sqrt(pi()).*x.^(1-n);
        part2 = hypergeom(1,[(1-n./2),(3/2-n./2)],-x.^2./4);
        part3 = gamma([(1-n/2),(3/2 - n/2)]);
        result = part1.*(part2./part3);
    end
end

However, the hypergeom function above (part2) is 2F1 which is regulized by the gamma function (part3). Which means the matrix dimentions do not aline.

Is there a method to create a 1F2 Regularized hypergeometric function within matlab? Or another way to calculate the fractional derivative of sin(x)?

Thanks in advanced.

[Walter Roberson]

https://www.mathworks.com/matlabcentral/fileexchange/5616-generalized-hypergeometric-function

https://www.mathworks.com/matlabcentral/answers/91324-regularized-hypergeometric-function-and-hypergeometric-function-syntax

https://groups.google.com/forum/#!topic/mpmath/Eia6qFimPNI

Answer 1

[David Goodmanson]

Hi Wozciech,

if you add a prod function,

part3 = prod(gamma([(1-n/2),(3/2 - n/2)]))

then you're good to go. Or, you could use the gamma duplication formula to replace your current part1/part3

part1/part3 =  x.^(1-n) * 2.^(n-1).*sqrt(pi) / (gamma(1-n/2)*gamma(3/2 - n/2))

with

part1/part3 = x.^(1-n) / gamma(2-n)