Incorrect results from hypergeom function in MATLAB R2018a.

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yann 2024-3-24

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https://ww2.mathworks.cn/matlabcentral/answers/2098051-incorrect-results-from-hypergeom-function-in-matlab-r2018a

评论： Dyuman Joshi 2024-4-19

采纳的回答： Amal Raj

In view of the following exact result:

2F1(1-n,1+n;3/2;1/2) =sin(nπ/2)/n

one would expect the result:

hypergeom([1−n,1+n],1.5,0.5)=0 if n is even.

However, for n=300, Matlab R2018a yields:

hypergeom([1−n,1+n],1.5,0.5)=Inf.

Why does this happen?

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Manikanta Aditya 2024-3-24

Mostly the issue here is due to the limitations of numerical precision and the way 'hypergeom' function handles larger inputs.

In your case, when n=300, the parameters of the hypergeom function become very large ([1−300,1+300]), which can lead to numerical instability and might result in MATLAB returning Inf.

If you need to compute the hypergeometric function for large parameters, you might need to use more specialized numerical methods or software that can handle such cases.

Thanks!

yann 2024-3-24

Thank all of you very much.

In MATLAB R2018b:

n = 300

>> hypergeom([1-n,1+n],1.5,0.5)

ans = -4.0076e-06

Nevertheless, In MATLAB R2016b, I obtain the correct answer:

n = 300

>> hypergeom([1-n,1+n],1.5,0.5)

ans = 0

How the disrepancy between MATLAB R2018b and MATLAB R2016a is explained?

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Answer 1

Amal Raj 2024-4-16

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https://ww2.mathworks.cn/matlabcentral/answers/2098051-incorrect-results-from-hypergeom-function-in-matlab-r2018a#answer_1441871

The difference is likely due to improvements or changes in MATLAB's numerical algorithms between versions R2016b and R2018b. While such discrepancies can be confusing, they often reflect efforts to improve the accuracy and reliability of numerical computations. For critical applications, it's always a good practice to check the release notes of MATLAB for any changes in numerical functions you rely on and to consider the implications of numerical precision and stability in your computations.

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Dyuman Joshi 2024-4-19

FYI - Release Notes for R2016b and R2018b are not available on the online MATLAB Release Notes documentation page. (The earliest one available right now is of R2019a, same as function documentations - only the information for last 5 years is available online)

I suppose one would have to contact the support team for that. And they would provide a better answer and clarification regarding the same as well, with appropriate information/explaination.

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