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On a family of symmetric hypergeometric functions of several variables and their Euler type integral representation. (English) Zbl 1290.33013

The authors consider a generalized hypergeometric series belonging to the Appell-Lauricella family of multiple series. The authors’ generalized series can also be considered as an example of Gelfand-Kapranov-Zelevinsky’s A-hypergeometric functions related to Aomoto’s theory of hypergeometric functions. A recurrence relation for the new series is obtained, and as a result, a representation in terms of multiple Euler-type integrals is also pointed out. Two particular cases of the new series are examined in detail.

MSC:

33C65 Appell, Horn and Lauricella functions
33C20 Generalized hypergeometric series, \({}_pF_q\)
33C70 Other hypergeometric functions and integrals in several variables
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