### Abstract

It is shown how a 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, Helmholz, and Schrodinger equations, and new bases can be constructed from the functions with which to expand general solutions of these physically important equations.

Original language | English (US) |
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Pages (from-to) | 69-89 |

Number of pages | 21 |

Journal | Studies in Applied Mathematics |

Volume | 66 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 1982 |

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## Cite this

Kalnins, E. G., Manocha, H. L., & Miller, W. (1982). HARMONIC ANALYSIS AND EXPANSION FORMULAS FOR TWO-VARIABLE HYPERGEOMETRIC FUNCTIONS.

*Studies in Applied Mathematics*,*66*(1), 69-89. https://doi.org/10.1002/sapm198266169