FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
2001, VOLUME 7, NUMBER 1, PAGES 71-86
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.
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Last modified: May 10, 2001