#16813: symbolic Legendre / associated Legendre functions / polynomials
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Reporter: rws | Owner:
Type: enhancement | Status: needs_review
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: |
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Comment (by mmezzarobba):
Replying to [comment:53 rws]:
> Replying to [comment:51 mmezzarobba]:
> > I find it strange that `Func_assoc_legendre_{P,Q}`derive from
`OrthogonalPolynomial` since these functions are not polynomials, even for
fixed integer m and n.
> https://en.wikipedia.org/wiki/Associated_Legendre_polynomials
> "...they satisfy the orthogonality condition..."
Sure, but they are not polynomials. It is necessarily wrong to use the
class `OrthogonalPolynomial` for things that are not, strictly speaking,
orthogonal polynomials if really necessary, but then there should at least
be a clear warning in the documentation of that class.
Replying to [comment:54 rws]:
> Of course, I'd rather have it all under functions/holonomic/...
I'm not sure being holonomic or not makes a big difference for a symbolic
function. What do you have in mind?
(As for me, I would like to have an implementation of general holonomic
functions in Sage at some point, but I'm more thinking of a parent
entirely separate from `SR` and with conversion methods to and from
symbolic functions. Symbolic functions that happen to be holonomic could
have a method that returns their representation using a system of linear
functional equations, and could use that to implement operations for which
no better function-specific code is available.)
--
Ticket URL: <http://trac.sagemath.org/ticket/16813#comment:55>
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