Spheroidal

spheroidal is a python library for computing spin weighted spheroidal harmonics along with their eigenvalues and derivatives. It supports both integer and half integer spin weights. The library provides implementations of the spherical expansion method described in (Hughes, 2000) and the continued fraction method from (Leaver, 1985). Also included is code for computing spin weighted spherical harmonics and spherical-spheroidal mixing coefficients. See the documentation for more information.

Installation

Install using Anaconda

   conda install -c conda-forge spheroidal

or using pip

   pip install spheroidal

Basic Usage

   import spheroidal
   from math import pi

   # Compute the spin weighted spheroidal eigenvalue with s = -2, l = 2, m = 2, gamma = 1.5
   spheroidal.eigenvalue(-2, 2, 2, 1.5)
   # -5.5776273646788255

   # Compute the corresponding spin weighted spheroidal harmonic
   S = spheroidal.harmonic(-2, 2, 2, 1.5)

   # Evaluate at theta = pi/2, phi = 0
   S(pi/2, 0)
   # (0.06692950919170575+0j)

   # Compute the derivative wrt theta at the same point
   spheroidal.harmonic_deriv(-2, 2, 2, 1.5)(pi/2, 0)
   # (-0.20852146386265577+0j)

Authors

• Seyong Park
• Zach Nasipak