harmonic_leaver_deriv2#

spheroidal.leaver.harmonic_leaver_deriv2(s, ell, m, g, num_terms, n_max=100)[source]#

Computes the second derivative with respect to theta of the spin-weighted spheroidal harmonic with spin-weight s, degree l, order m, and spheroidicity g using Leaver’s method.

Parameters:

  • s (int or half-integer float) – spin weight

  • ell (int or half-integer float) – degree

  • m (int or half-integer float) – order

  • g (complex) – spheroidicity

  • num_terms (int) – number of terms in the expansion

  • n_max (int) – maximum number of terms in the expansion

Returns:

second derivative of the spin-weighted spheroidal harmonic \(\frac{d^2}{d\theta^2}\left({}_{s}S_{lm}(\theta,\phi)\right)\)

Return type:

function