sphPlm_deriv(lmax, x)

Normalized associated Legendre function for spherical harmonics, with derivative.

[y, d] = sphPlm_deriv(lmax, x)
Computes the normalized associated Legendre polynomial
\sqrt{(2l+1)/(4\pi)} \sqrt{(l-m)!/(l+m)!} P_l^m(x)
and its derivative, suitable for use in spherical harmonics, for l=0,...,lmax and m=0,...,l.
Vectorized in x, returns matrix with scaled P_l^m(x) at y(:, l+1,m+1) and scaled d/dx P_l^m(x) at d(:, l+1,m+1).
Based on recursion formulas found in:
W.H. Press, Numerical Recipes 3rd edition, p. 292
T. Limpanuparb, J. Milthorpe, arXiv:1410.1748v1 [physics.chem-ph]
using the implementation gsl_sf_legendre_sphPlm_deriv_array found in the Gnu Scientific Library as a template.