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Added an implementation of Legendre polynomial computation algorithm #12406

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@Nanoemm Nanoemm commented Dec 3, 2024

Describe your change:

This implementation provides a method to compute the coefficients of Legendre polynomials of degree n. Legendre polynomials are a sequence of orthogonal polynomials widely used in physics and engineering, particularly in solving differential equations and performing spherical harmonic expansions. The algorithm uses a recursive relation to derive the coefficients efficiently, ensuring numerical stability and correctness.
https://en.wikipedia.org/wiki/Legendre_polynomials

  • Add an algorithm?
  • Fix a bug or typo in an existing algorithm?
  • Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request.
  • Documentation change?

Checklist:

  • I have read CONTRIBUTING.md.
  • This pull request is all my own work -- I have not plagiarized.
  • I know that pull requests will not be merged if they fail the automated tests.
  • This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
  • All new Python files are placed inside an existing directory.
  • All filenames are in all lowercase characters with no spaces or dashes.
  • All functions and variable names follow Python naming conventions.
  • All function parameters and return values are annotated with Python type hints.
  • All functions have doctests that pass the automated testing.
  • All new algorithms include at least one URL that points to Wikipedia or another similar explanation.
  • If this pull request resolves one or more open issues then the description above includes the issue number(s) with a closing keyword: "Fixes #ISSUE-NUMBER".

Nanoemm and others added 12 commits November 20, 2024 09:59
Changed argument name A to a
Changed variable name V to v
Added specifications for beta and alpha
Changed np.random.randn
…e_pablo

# Conflicts:
#	linear_algebra/lanczos_algorithm.py
Added an algorithm that calculates the coefficients of the Legendre polynomial of degree n using the recurrence relation.
Added an algorithm that calculates the coefficients of the Legendre polynomial of degree n using the recurrence relation.
@Nanoemm Nanoemm closed this Dec 3, 2024
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