FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2001, VOLUME 7, NUMBER 1, PAGES 71-86

**Analytical continuation formulas for multiple hypergeometric series**

A. W. Niukkanen

Abstract

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Applying canonical forms of multiple hypergeometric series along with
the use of the operator factorization method makes it
possible to obtain, in explicit and most general form,
the analytical continuation formulas directly applicable to
arbitrary series having the Gaussian type ($2//1$) with respect to one
or several arguments.
The formulas help us to unify a great number of particular
formulas scattered throughout the literature.
Moreover they give us a complete set of relations for any
non-standard series provided that it pertains to the Gaussian
type with respect to at least one of its variables.
Due to simplicity and universality of the basic relations there
arises an important possibility to implement computer-aided
analysis of numerous repeated transformations with respect to
different arguments of the series and to join these
transformations with other important types of transformations.
This possibility may have significance for mathematical analysis,
mathematical physics, computer algebra and theoretical chemistry.

All articles are
published in Russian.

Location: http://mech.math.msu.su/~fpm/eng/k01/k011/k01105h.htm

Last modified: May 10, 2001