Unfortunately, I am not familiar with the details either.
Nevertheless, I have made the proposed change for the interval -1https://mathworld.wolfram.com/AssociatedLegendrePolynomial.html. Most
importantly, this also solves the problem with spherical harmonics, which
was the a highly requested
Hi,
Le mardi 27 mars 2018 14:46:52 UTC+2, Ralf Stephan a écrit :
>
>
> I think it will suffice for now to put the fact in the documentation.
>
I am afraid this is not sufficient: a consequence of this bug is that Sage
gives a silly answer for something as elementary as the spherical harmonic
On Tuesday, March 27, 2018 at 11:20:02 AM UTC+2, James Womack wrote:
>
> I have created a ticket on Sage trac for this issue:
> https://trac.sagemath.org/ticket/25034
>
Thanks.
> As I mention in the ticket, I think that this issue raises a question as
> to whether the Func_assoc_legendre_P
I have created a ticket on Sage trac for this issue:
https://trac.sagemath.org/ticket/25034
As I mention in the ticket, I think that this issue raises a question as to
whether the Func_assoc_legendre_P class is correctly defined, given that it
now seems to cover both the Ferrers and associated
Oh, by the way, Wolfram Mathworld is just completely wrong on this page you
referenced.
There is a huge difference between the two functions.
Also, there is no such thing as an associated Legendre polynomial.
There is a Legendre polynomials, but if you take the degrees and orders to
be integers
The Ferrers functions are defined on the real segment (-1,1).
The associated Legendre functions are in general defined on the Complex
plane except for the ray (-\infty,1].
Typically Ferrers functions are written with argument x=\cos\theta, |x|<1
and associated Legendre functions are written
Thanks. If that is the case, then presumably this *is* a bug in Sage Math
and Func_assoc_legendre_P should distinguish the special cases for n == m
when x > 1 or x < 1 when evaluating associated Legendre polynomials.
Would you be able to clarify the distinction between Ferrers functions of
the
On Thursday, March 22, 2018 at 3:25:06 AM UTC-7, Samuel Lelievre wrote:
>
> Ralf wrote:
> > Thanks,
> > P.S. Still someone should contact DLMF with the right arguments.
>
> I just emailed them with cc to sage-devel.
>
There's nothing wrong with the formula. The Legendre function in the DLMF
Thanks. I am waiting for an account on Sage trac, then I will submit a bug
report.
On Thursday, 22 March 2018 10:25:06 UTC, Samuel Lelievre wrote:
>
> Ralf wrote:
> > Thanks,
> > P.S. Still someone should contact DLMF with the right arguments.
>
> I just emailed them with cc to sage-devel.
>
Ralf wrote:
> Thanks,
> P.S. Still someone should contact DLMF with the right arguments.
I just emailed them with cc to sage-devel.
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arb agrees here:
sage: CBF(1/2).legendre_P(1,1)
[-0.8660254037844386 +/- 5.90e-17]
So I'd suggest using complex balls for your numerics until the bug is fixed.
Thanks,
P.S. Still someone should contact DLMF with the right arguments.
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