Incorrect results from hypergeom function in MATLAB R2018a.

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?

[Dyuman Joshi]

Can you share a picture of the result, along with the code?

FYI, the results in R2023b are as follows -

n=300;
%numeric function
hypergeom([1-n,1+n],1.5,0.5)

ans = -4.0076e-06

%symbolic function
hypergeom(sym([1-n,1+n]), sym(1.5), sym(0.5))

ans = 

0

[Manikanta Aditya]

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]

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?

Answer 1

[Amal Raj]

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.

[Dyuman Joshi]

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.