Re: [Help-gsl] sign in gsl_sf_legendre_Plm / gsl_sf_legendre_sphPlm

[Patrick Alken]

On 10/29/2014 12:33 PM, Denis Davydov wrote:
> Dear all,
>
> I am trying to use the associated Legendre polynomials,
> but I am confused about the sign.
> I would expect P_1^1(cos(phi)) = sin(phi) > 0 and
> therefore to have the normalised polynomial also positive.
> However, it seems that there is a (-1)^m multiplier
> compared to the expression I see in several books.
> Could someone please clarify this issue for me?
>
> Kind regards,
> Denis
As stated in the documentation, GSL follows Abramowitz and Stegun, and 
you can see from eq 8.6.6 of their book that the (-1)^m factor is 
included in the definition, so P11 = -sin(theta)