Unfortunately, I am not familiar with the details either.

Nevertheless, I have made the proposed change for the interval -1<x<1 and 
for now left the name of associated Legendre polynomials even if that might 
not be rigorously correct. But at least this terminology is in line with 
https://mathworld.wolfram.com/AssociatedLegendrePolynomial.html. Most 
importantly, this also solves the problem with spherical harmonics, which 
was the a highly requested fix.

As for resolving the convention conflicts in a rigorous manner I propose a 
follow-up ticket: https://trac.sagemath.org/ticket/31637.

Best,
Michael

Eric Gourgoulhon schrieb am Sonntag, 8. April 2018 um 18:07:56 UTC+2:

> 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 
> Y_1^1(theta, phi), see  
> https://trac.sagemath.org/ticket/25034#comment:3
>
> Best wishes,
>
> Eric.
>

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