On Warnaar's elliptic matrix inversion and Karlsson-Minton-type elliptic hypergeometric series

Details On Warnaar's elliptic matrix inversion and Karlsson-Minton-type elliptic hypergeometric series On Warnaar's elliptic matrix inversion and Karlsson-Minton-type elliptic hypergeometric series

2003-09-22

arxiv.org/abs/math/0309358v1

J. Comput. Appl. Math. 178 (2005), 377-391

Mathematics

Classical Analysis and ODEs

16 pages

Scientific paper

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.

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