#16813: symbolic Legendre / associated Legendre functions / polynomials
-------------------------------------+-------------------------------------
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):
Hi!
We have several possible ways out of this:
1) avoid recursion for symbolic argument for Legendre_Q and use another
library (maxima, flint, sympy ... ) for evaluation.
2) Let it be, but avoid it as default method.
3) Maybe more elegantly: There is a more closed relation for legendre_Q
(but it's not really a recursion):
{{{
Q(n,z) = ½P(n,z) ln((z+1)/(z-1)) - W(n-1,z)
}}}
with
{{{
W(n,z) = Σ_{k=1}^n (1/k) P(k-1,z) P(n-k,z)
}}}
(Gradshteyn-Ryzhik p 1019f)
Hope this could be of some use
--
Ticket URL: <http://trac.sagemath.org/ticket/16813#comment:18>
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