Elementary derivations of summation and transformation formulas for $q$-series.
Author: George Gasper
Abstract:
We present some elementary derivations of summation
and transformation formulas for $q$-series, which are different
from, and in several cases simpler or shorter than,
those presented in the G. Gasper and M. Rahman
``Basic Hypergeometric Series'' book,
the W.N. Bailey ``Generalized Hypergeometric Series''
and L.J. Slater ``Generalized Hypergeometric Functions''
books, and in some papers;
thus providing deeper insights into the theory of $q$-series.
Our main emphasis is on
methods that can be used to
{\bf derive} formulas, rather than
to just {\it verify} previously derived or conjectured formulas.
This approach leads to the derivation of a new family of summation
formulas for very-well-poised basic hypergeometric series
${}_{6+2k}W_{5+2k} \,, \ k= 1, 2, \ldots .$
Published in
Fields Institute Communications 14 (1997), 55-70..
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