#16813: symbolic Legendre / associated Legendre functions / polynomials
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Reporter: rws | Owner:
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-6.6
Component: symbolics | Resolution:
Keywords: | Merged in:
Authors: Ralf Stephan, | Reviewers:
Stefan Reiterer | Work issues:
Report Upstream: N/A | Commit:
Branch: | 9df78de81e0c307a1181a6ad4453bc56a93870b2
u/rws/symbolic_legendre___associated_legendre_functions___polynomials|
Stopgaps:
Dependencies: #17953 |
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Description changed by rws:
Old description:
> Existing numeric functions are `legendre_P`, `legendre_Q`,
> `gen_legendre_P`, and `gen_legendre_Q` which correspond to P(n,x) /
> Q(n,x) and associated Legendre P(n,m,x) / Q(n,m,x).
>
> They should be made symbolic. FLINT has fast code for P(n,x).
>
> * PQ(n,x)
> * https://en.wikipedia.org/wiki/Legendre_polynomials
> * http://mathworld.wolfram.com/LegendrePolynomial.html
> * PQ(n,m,x)
> * https://en.wikipedia.org/wiki/Associated_Legendre_polynomials
> * http://mathworld.wolfram.com/AssociatedLegendrePolynomial.html
> * functions PQ
> * https://en.wikipedia.org/wiki/Legendre_function
> * http://mathworld.wolfram.com/LegendreFunctionoftheFirstKind.html
> * http://mathworld.wolfram.com/LegendreFunctionoftheSecondKind.html
New description:
Existing numeric functions are `legendre_P`, `legendre_Q`,
`gen_legendre_P`, and `gen_legendre_Q` which correspond to P(n,x) / Q(n,x)
and associated Legendre P(n,m,x) / Q(n,m,x).
They should be made symbolic. FLINT has fast code for P(n,x).
* PQ(n,x)
* https://en.wikipedia.org/wiki/Legendre_polynomials
* http://mathworld.wolfram.com/LegendrePolynomial.html
* PQ(n,m,x)
* https://en.wikipedia.org/wiki/Associated_Legendre_polynomials
* http://mathworld.wolfram.com/AssociatedLegendrePolynomial.html
* functions PQ
* https://en.wikipedia.org/wiki/Legendre_function
* http://mathworld.wolfram.com/LegendreFunctionoftheFirstKind.html
* http://mathworld.wolfram.com/LegendreFunctionoftheSecondKind.html
See also http://ask.sagemath.org/question/27230/problem-with-
hypergeometric/
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Ticket URL: <http://trac.sagemath.org/ticket/16813#comment:64>
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