Hypergeometric functions(1F2) in matlab

Question

ALI 2024-6-11

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2127431-hypergeometric-functions-1f2-in-matlab

评论： Walter Roberson 2024-6-11

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?

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ALI 2024-6-11

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

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Answer 1

Walter Roberson 2024-6-11

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https://ww2.mathworks.cn/matlabcentral/answers/2127431-hypergeometric-functions-1f2-in-matlab#answer_1470431

在 MATLAB Online 中打开

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

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ALI 2024-6-11

在 MATLAB Online 中打开

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 2024-6-11

在 MATLAB Online 中打开

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.

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Answer 2

Shivani 2024-6-11

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2127431-hypergeometric-functions-1f2-in-matlab#answer_1470201

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.

Hope this helps!

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ALI 2024-6-11

在 MATLAB Online 中打开

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 