FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

1999, VOLUME 5, NUMBER 3, PAGES 717-745

**A new theory of multiple hypogeometric series and its prospects
for computer algebra programming**

A. W. Niukkanen

Abstract

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We first give a brief overview of basic concepts and calculational techniques
of the operator factorization method which provides a simple and universal
foundation for a new theory of hypergeometric series in any number of
variables. Notation, factorization formulas and all auxiliary identities
used in the paper are given in section 2, 3 and 4, respectively. The most
essential constituents are: illustrative examples showing how the
method works in practice (section 5); new transformation theory of multiple
hypergeometric series (section 6); the prospects of the method including
applications to computer algebra systems and discussion of the position
occupied by the new method amongst other approaches to the theory of
hypergeometric series (section 7).
The conclusion of practical importance is that the factorization method
is the only method allowing us to develop active
knowledge-based computer
programs rather than the passive data bases typical for traditional
approaches. In other words the new method holds out a hope for programs
capable to synthesize the formulas at the moment they are needed by
the user.
```

All articles are
published in Russian.

Location: http://mech.math.msu.su/~fpm/eng/99/993/99305t.htm

Last modified: November 11, 1999