Hypergeometric functions(1F2) in matlab

ALI
2024 6 11
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更新时间：2024 6 11
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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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Walter Roberson
Walter Roberson 2024-6-11

1 个投票

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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Walter Roberson
Walter Roberson 2024-6-11
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
ALI 2024-6-11
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
Walter Roberson 2024-6-11
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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Shivani
Shivani 2024-6-11

0 个投票

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
ALI 2024-6-11
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

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