On Warnaar's elliptic matrix inversion and Karlsson-Minton-type elliptic hypergeometric series
arXiv:math/0309358 · doi:10.1016/j.cam.2004.02.028
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.
16 pages
References in corpus (1)
Cited by in corpus (5)
- Essays on the theory of elliptic hypergeometric functions
- Theta Functions, Elliptic Hypergeometric Series, and Kawanaka's Macdonald Polynomial Conjecture
- Elliptic Littlewood identities
- Multidimensional Matrix Inversions and Elliptic Hypergeometric Series on Root Systems
- Duality transformation formulas for multiple elliptic hypergeometric series of type