add comments on instability issue

[ajarifi]

This is a pull request related to #101.

Add some notes on numerical stability for several related polynomials.

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 87.36%. Comparing base (f0e80dc) to head (f0a6587).
⚠️ Report is 19 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #136      +/-   ##
==========================================
+ Coverage   87.30%   87.36%   +0.06%     
==========================================
  Files          11       11              
  Lines         378      380       +2     
==========================================
+ Hits          330      332       +2     
  Misses         48       48              

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[ohno]

This is a pull request related to #101.

I think that comment is generally fine (what we needed). But I'm not sure that Laguerre polynomials, Legendre polynomials, and Hermitian polynomials have been sufficiently tested.

[ajarifi]

FYI, when I tested the polynomials again. Related to #97, #143, the generalized Laguerre polynomials still contain $\alpha$, and spherical harmonics also contain $\theta$ and $\phi$.

[ajarifi]

I wonder if, for HO potential, the Hermite polynomial should replace the Laguerre polynomial.

[ajarifi]

In #146, I compare the results obtained from the recurrence relation and the closed form. Evidently, they give consistent results for up to $n=10$. Therefore, the results from the closed form are reliable up to $n=10$. Above that number, there are some problems, such as the need for $n=big(number)$, instability, etc. As a future development, the recurrence relation can be used.

[ohno]

Sufficient testing has been done at #146.
Close #101
Close #146