J Austral Math Soc Ser B 37 pp212--234, 1995.

Derivatives of addition theorems for Legendre functions

D. E. Winch and P. H. Roberts

(Received 1 March 1994; revised 28 May 1994)

Abstract

Differentiation of the well-known addition theorem for Legendre polynomials produces results for sums over order m of products of various derivatives of associated Legendre functions. The same method is applied to the corresponding addition theorems for vector and tensor spherical harmonics. Results are also given for Chebyshev polynomials of the second kind, corresponding to 'spin-weighted' associated Legendre functions, as used in studies of distributions of rotations.

Browse the article

Read the article in your browser. (Print at 75% on A4 paper).

Authors

D. E. Winch: Department of Applied Mathematics, University of Sydney, Sydney, 2006, Australia.
P. H. Roberts: Institute of Geophysics and Planetary Physics, Los Angeles, California, 90024, U.S.A.