On a relation between spherical and spheroidal harmonics

H. A. Buchdahl*, N. P. Buchdahl, P. J. Stiles

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)


Expressions are found for the coefficients in the relations which exhibit spheroidal harmonics as linear combinations of spherical harmonics and vice versa. In particular it is shown that in the case of prolate spheroidal harmonics the non-vanishing coefficients kLMl in the relation P L M(u)PL M( nu )= Sigma ikLMlrlPl M(cos theta ) are given by kLMl=(-1)(L-l)2/2-La -l(L+M)!(L+l)!/(L-M)!(l+M)!(1/2L+1/2l)!(1/2l-1/2l)!, where l=L, L-2, L-4,...,M' with M'=M or M+1 according as L-M is even or odd, respectively.

Original languageEnglish
Pages (from-to)1833-1836
Number of pages4
JournalJournal of Physics A: Mathematical and General
Issue number11
Publication statusPublished - 1977
Externally publishedYes


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