Hypergeometric functions(1F2) in matlab

I want to use the hypergeometric function [def] this exists in mathematica (wolfram). I tried this

function result = hypegeo(q, r)
qr = q * r;
z = - (qr)^2 / 4; 
inp=[3/2,[1, 5/2],z];
F2_value = hypergeom(1,2,inp);
result = (1/3) * F2_value;
end

but for me looking at the definition of the hyper geometric function in matlab doesnt seem exaclty the same as the one in wolfram.

if they arent the same, is there a way to use mathmatica functions in matlab or some other workaround for this?

[ALI]

i found Hypergeometric functions — mpmath 1.3.0 documentation , how can I use it in matlab?

Answer 1

[Walter Roberson]

In MATLAB, some of the parameters are implicit according to the length of the other parameters.

function result = hypegeo(q, r)
    qr = q * r;
    z = - (qr)^2 / 4; 
    F2_value = hypergeom(3/2, [1, 5/2], z);
    result = (1/3) * F2_value;
end

[Walter Roberson]

Reminder:

inp=[3/2,[1, 5/2],z];

means the same as

inp = horzcat(3/2, [1, 5/2], z)

which is the same as

inp = horzcat(3/2, horzcat(1, 5/2), z);

which simplifies to

inp = horzcat(3/2, 1, 5/2, z)

Using [] is a shortcut to list concatenation, and everything will get "flattened". [] inside of [] does not result in the inner [] elements being grouped together somehow.

The syntax for creating groups would be

inp = {3/2,[1, 5/2],z};

However, hypergeom() does not accept cell arrays.

[ALI]

Thanks for the explanation, a small question in case I wanted to use a python function for general knowledge,

as an example, is this a correct way to do it?

function result = hypegeo(q, r)
py=pyenv(Version='directory');
py
% Define parameters
a = 3/2;
b = 1;
c = 5/2;
z = -1*((q*r)^2)/4;
% Call mpmath's hyp1f2 function
result_py = py.pyrun(mpmath.hyper(a, b, c, z));
% Convert Python result to MATLAB double
result = double(result_py);
end

[Walter Roberson]

No, mpmath.hyper accepts a, b, z parameters, where a and b are tuples. There is no hyper(a, b, c, z)

You should be using

a = 3/2;
b1 = 1;
b2 = 5/2;
z = -1*((q*r)^2)/4;
result_py = py.pyrun(mpmath.hyp1f2(a, b1, b2, z));

or something similar.

Answer 2

[Shivani]

Hello @ALI,

You can refer to the following file exchange link for implementation details of calculating a generalized Hypergeometric function: https://www.mathworks.com/matlabcentral/fileexchange/5616-generalized-hypergeometric-function

Additionally, the following MATLAB Answer threads also provide details on implementing a Hypergeometric function in MATLAB.

• https://www.mathworks.com/matlabcentral/answers/570436-regularized-hypergeometric-function-1f2-within-matlab
• https://www.mathworks.com/matlabcentral/answers/91324-regularized-hypergeometric-function-and-hypergeometric-function-syntax

Hope this helps!

[ALI]

function result = hypegeo(q, r)
py=pyenv(Version='directory');
py
% Define parameters
a = 3/2;
b = 1;
c = 5/2;
z = -1*((q*r)^2)/4;
% Call mpmath's hyp1f2 function
result_py = py.pyrun(mpmath.hyper(a, b, c, z));
% Convert Python result to MATLAB double
result = double(result_py);
end 

I tried this I think its correct but it gives an errorr with loading python functions