S(s=-2, l=2, gamma=1.9)

The SpinWeightedSpheroidalHarmonics package for Mathematica provides functions for computing spin-weighted spheroidal harmonics, spin-weighted spherical harmonics and their associated eigenvalues. Support is included for both arbitrary-precision numerical evaluation, and for series expansions.

Getting the package

The latest development version will always be available from the project git repository:

git clone https://github.com/BlackHolePerturbationToolkit/SpinWeightedSpheroidalHarmonics.git


The SpinWeightedSpheroidalHarmonics package requires a recent version of Mathematica. It is typically tested with only the latest available version.


Clone the repository and place it somewhere on Mathematica’s $Path. Typical locations are inside ${HOME}/.Mathematica/Applications/ for Linux or inside ${HOME}/Library/Mathematica/Applications/ for Mac OSX.


The package may be loaded into Mathematica using the command:

<< SpinWeightedSpheroidalHarmonics`


Examples are included in the documentation. See the SpinWeightedSpheroidalHarmonics page in Documentation Center.

Known problems

Known bugs are recorded in the project bug tracker.


This code is distributed under the University of Illinois/NCSA Open Source License. Details can be found in the LICENSE file.


Barry Wardell
Niels Warburton
Marc Casals
Sarp Akcay

Citation Guideline

If you make use of any of the Toolkit in your research please acknowledge using:

This work makes use of the Black Hole Perturbation Toolkit.