#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:
-------------------------------------+-------------------------------------
Comment (by rws):
Also, your recursive functions for `Q(n,x)` and `Q(n,m,x)` appear to be
wrong:
{{{
sage: legendre_Q.eval_recursive(2,x).subs(x=3)
13/2*I*pi + 13/2*log(2) - 9/2
sage: legendre_Q.eval_recursive(2,x).subs(x=3).n()
0.00545667363964419 + 20.4203522483337*I
sage: legendre_Q(2,3.)
0.00545667363964451 - 20.4203522483337*I
}}}
The latter result from mpmath is supported by Wolfram.
As to `Q(n,m,x)`:
{{{
sage: gen_legendre_Q(2,1,x).subs(x=3)
-1/8*sqrt(-2)*(72*I*pi + 72*log(2) - 50)
sage: gen_legendre_Q(2,1,x).subs(x=3).n()
39.9859464434253 + 0.0165114736149170*I
sage: gen_legendre_Q(2,1,3.)
-39.9859464434253 + 0.0165114736149193*I
}}}
Again, Wolfram supports the latter value from mpmath (symbolic as `(25
i)/(2 sqrt(2))-18 i sqrt(2) ((log(4))/2+1/2 (-log(2)-i pi))`).
--
Ticket URL: <http://trac.sagemath.org/ticket/16813#comment:14>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
--
You received this message because you are subscribed to the Google Groups
"sage-trac" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To post to this group, send email to [email protected].
Visit this group at http://groups.google.com/group/sage-trac.
For more options, visit https://groups.google.com/d/optout.
