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On confluences of the general hypergeometric systems. (English) Zbl 0822.33007
The paper extends the previous work of the authors in which they have introduced the so-called generalized confluent hypergeometric (CHG) functions. These functions are defined as solutions of certain systems of partial differential equations on a finite dimensional complex vector space. As a special case, CHG functions include the general hypergeometric functions studied by K. Aomoto and I. M. Gel’fand. The main result of the article is that the system of equations for CHG functions can be obtained from the system for Aomoto-Gel’fand functions by a finite number of certain limit processes. The classical analogue of this result is a limit process that reduces the equation for hypergeometric (Gauss) functions into the equation for degenerate hypergeometric (Kummer) functions.

MSC:
33C70 Other hypergeometric functions and integrals in several variables
33C15 Confluent hypergeometric functions, Whittaker functions, \({}_1F_1\)
Keywords:
limit processes
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