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Lie Theory and Generalizations of the Hypergeometric Functions

Willard Miller, Jr.
SIAM Journal on Applied Mathematics
Vol. 25, No. 2 (Sep., 1973), pp. 226-235
Stable URL: http://www.jstor.org/stable/2099942
Page Count: 10
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Lie Theory and Generalizations of the Hypergeometric Functions
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Abstract

In this paper we use the differential recurrence relations satisfied by the 2F1 and their generalizations the pFq and Lauricella functions to associate a Lie algebra (dynamical symmetry algebra) with each of these families of special functions. We demonstrate that the representation theory of the Lie algebras yields a variety of addition theorems and generating functions for the associated families. Most of the results of this survey are contained in the author's papers [1]-[3] but the comments on the functions FA, FB, FC are new.

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