#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:
u/rws/symbolic_legendre___associated_legendre_functions___polynomials|
0f86b77a9aa818add6848cacf9a3f371d49c7d3a
Dependencies: | Stopgaps:
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Comment (by maldun):
Replying to [comment:12 rws]:
> Replying to [comment:5 maldun]:
> > I already implemented all Orthopolys one time:
http://trac.sagemath.org/attachment/ticket/9706/trac_9706_ortho_polys.patch
> >
> > they only would need cleanup/restructuring. Maybe you can reuse some
of the implemented methods (like recursions and derivatives)
> I am not sure about the derivatives. For `P(3,2,x).diff(x)` I get
`-45*x^2 + 15` (Wolfram agrees) while with your formula (lines 2377-2395
of the patch) I get (after simplification) `-45*x^2 - 15`.
>
> Update: what's your reference there?
It seems you are right. from Gradshteyn-Ryzhik p.1004 formula 8.731-1 we
have the relation
{{{
P(n,m,x).diff(x) = ((n+1-m)*P(n+1,m,x)-(n+1)*x*P(n,m,x))/(x**2-1)
}}}
The same relation holds for gen_legendre_Q
I suppose that's an copy/paste/rewrite mistake from my side.
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Ticket URL: <http://trac.sagemath.org/ticket/16813#comment:13>
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