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Harmonic Analysis and Expansion Formulas for Two‐Variable Hypergeometric Functions
Author(s) -
Kalnins E. G.,
Manocha H. L.,
Miller Willard
Publication year - 1982
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm198266169
Subject(s) - mathematics , hypergeometric function , laplace transform , generalized hypergeometric function , helmholtz equation , variable (mathematics) , harmonic function , mathematical analysis , confluent hypergeometric function , special functions , laplace's equation , pure mathematics , partial differential equation , boundary value problem
The authors show how their Lie‐theoretic characterization of two‐variable hypergeometric functions can be employed to derive expansion theorems involving these functions. In particular, the functions arise as solutions of the Laplace, wave, heat, Helmholtz, and Schrooinger equations, and new bases can be constructed from the functions with which to expand general solutions of these physically important equations.