A class of generalised multiple hypergeometric series arising in physical and quantum chemical applications

The multivariable hypergeometric function nF(x1, . . . , xn), considered recently by Niukkanen (1984), is a straightforward generalisation of certain well known hypergeometric functions of n variables; indeed it provides a unification of the generalised hypergeometric function pFq of one variable, Appell and Kampe de Feriet functions of two variables, and Lauricella functions of n variables, as well as of many other hypergeometric series which arise naturally in physical and quantum chemical applications. The author derives several interesting properties of this multivariable hypergeometric function (including, for example, many which were not given by Niukkanen) as useful consequences of substantially more general results available in the literature.

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