Harmonic Analysis and Expansion Formulas for Two-Variable Hypergeometric Functions

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.