Special functions and the complex Euclidean group in 3-space. I

Willard Miller

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


It is shown that the general addition theorems of Gegenbauer, relating Bessel functions and Gegenbauer polynomials, are special cases of identities for special functions obtained from a study of certain local irreducible representations of the complex Euclidean group in 3-space. Among the physically interesting results generalized by this analysis are the expansion for a plane wave as a sum of spherical waves and the addition theorem for spherical waves. This paper is one of a series attempting to derive the special functions of mathematical physics and their basic properties from the representation theory of Lie symmetry groups.

Original languageEnglish (US)
Pages (from-to)1163-1175
Number of pages13
JournalJournal of Mathematical Physics
Issue number8
StatePublished - 1968
Externally publishedYes


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