Condon-Shortley Phase Factor #93
Description
According to the documentation for Plm (https://docs.juliahub.com/SphericalHarmonics/NjDk0/0.1.14/#SphericalHarmonics.computePlmcostheta-Tuple{Any}) and for the spherical harmonics Ylm (https://docs.juliahub.com/SphericalHarmonics/NjDk0/0.1.14/#SphericalHarmonics.computeYlm ) the C-S factor (-1)^m is not included in the definitions. However, that's not what I am observing. For example, the formula for Y21 with the C-S factor is given by
Y21 (theta, phi) = (-)sqrt(15/32pi) sin(2*theta) exp(i phi).
For theta=pi/3, phi=0, it gives a value of -0.3345232717786446.
Now following code produces exactly the same value:
ynm = computeYlm(pi/3,0.0,lmax=2); ynm[(2,1)]
-0.33452327177864466 - 0.0im
I have verified the same behavior for Y(1,1) as well.
Is it possible that the documentation is incorrect? Or am I missing something? [I can think of another possibility, the branch used in defining (1-x^2)^{m/2}) in the definition of Pnm.]
Could you please clarify?
Thanks,
Sanjay Velamparambil