On Warnaar's elliptic matrix inversion and
Karlsson-Minton-type elliptic hypergeometric series
(15 pages)
Abstract.
Using Krattenthaler's
operator method, we give a new proof of
Warnaar's
recent elliptic extension of Krattenthaler's matrix inversion.
Further, using a theta function identity closely related to Warnaar's
inversion, we derive summation and transformation formulas for
elliptic hypergeometric series of Karlsson-Minton-type.
A special case yields a particular summation that was used by Warnaar to
derive quadratic, cubic and quartic transformations for elliptic hypergeometric
series. Starting from another theta function identity, we derive yet different
summation and transformation formulas for elliptic hypergeometric series of
Karlsson-Minton-type. These latter identities seem quite unusual and appear to
be new already in the trigonometric (i.e., p = 0) case.
The following versions are available:
Back to Michael Schlosser's
home page.