#16813: symbolic Legendre / associated Legendre functions / polynomials
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Reporter: rws | Owner:
Type: enhancement | Status: new
Priority: major | Milestone: sage-6.4
Component: symbolics | Resolution:
Keywords: | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Comment (by maldun):
Replying to [comment:3 rws]:
> OK I have a question. What is the equivalent recursive algorithm to
https://github.com/sagemath/sage/blob/master/src/sage/functions/orthogonal_polys.py#L812-834
> for Legendre polynomials?
>
> The link is valid as long #16812 is not merged.
Hi!
You won't have luck to find an equivalent recursion algorithm for Legendre
Polynomials, since the recursion algorithm for Chebyshev Polynomials uses
the fact that cheby polynomials are cosines in disguise, and thus one is
able to build Cheby polyis in O(log N) time. For Legendre polynomials you
have to use the classic recursion formula given in
[https://en.wikipedia.org/wiki/Legendre_polynomials#Recursive_definition]
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Ticket URL: <http://trac.sagemath.org/ticket/16813#comment:4>
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