harmonic_deriv#

spheroidal.wrapper.harmonic_deriv(s, ell, m, g, n_theta=1, n_phi=0, method='spectral', num_terms=None, n_max=100)[source]#

Computes the derivative of the spin-weighted spheroidal harmonic with spin-weight s, degree l, order m, and spheroidicity g.

Supported methods:

  • “spectral” (default): uses the spherical expansion method described in Appendix A of

    (Hughes, 2000)

  • “leaver”: uses the continued fraction method described in

    (Leaver, 1985)

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

  • method (str, optional) – method used to compute the harmonic, defaults to “spectral”

  • n_theta (int, optional) – number of derivatives with respect to theta (options are 0, 1 and 2), defaults to 1

  • n_phi (int, optional) – number of derivatives with respect to phi, defaults to 0

  • num_terms (int, optional) – number of terms used in the expansion, automatic by default

  • n_max (int, optional) – maximum number of terms in the expansion, defaults to 100

Returns:

spin-weighted spheroidal harmonic \({}_{s}S_{lm}(\theta,\phi)\) differentiated n_theta times with respect to theta and n_phi times with respect to phi

Return type:

function