TY - JOUR
T1 - On a relation between spherical and spheroidal harmonics
AU - Buchdahl, H. A.
AU - Buchdahl, N. P.
AU - Stiles, P. J.
PY - 1977
Y1 - 1977
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=0040907907&partnerID=8YFLogxK
U2 - 10.1088/0305-4470/10/11/011
DO - 10.1088/0305-4470/10/11/011
M3 - Article
AN - SCOPUS:0040907907
SN - 0305-4470
VL - 10
SP - 1833
EP - 1836
JO - Journal of Physics A: Mathematical and General
JF - Journal of Physics A: Mathematical and General
IS - 11
ER -