leaver

Module containing functions for computing spin-weighted spheroidal harmonics using Leaver’s method.

Functions

continued_fraction(A, s, ell, m, g[, n_max])	Evaluates the continued fraction in equation 21 of (Leaver, 1985) until it converges to machine precision using the modified version of Lentz's method described in https://duetosymmetry.com/notes/take-derivative-continued-fraction/.
continued_fraction_deriv(A, s, ell, m, g[, ...])	Evaluates the derivative of the continued fraction in equation 21 of (Leaver, 1985) until it converges to machine precision using automatic differentiation of Lentz's method as described in https://duetosymmetry.com/notes/take-derivative-continued-fraction/.
eigenvalue_leaver(s, ell, m, g)	Computes the spin weighted spheroidal eigenvalue with spin-weight s, degree l, order m, and spheroidicity g using the continued fraction method described in (Leaver, 1985).
harmonic_leaver(s, ell, m, g[, num_terms, n_max])	Computes the spin-weighted spheroidal harmonic with spin-weight s, degree l, order m, and spheroidicity g using Leaver's method.
harmonic_leaver_deriv(s, ell, m, g[, ...])	Computes the 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.
harmonic_leaver_deriv2(s, ell, m, g, num_terms)	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.
leaver_coefficients(s, ell, m, g[, ...])	Computes the coefficients of the Frobenius expansion in equation 18 of (Leaver, 1985)