Summation and transformation formulas for elliptic hypergeometric series

Abstract

Using matrix inversion and determinant evaluation techniques we prove several summation and transformation formulas for terminating, balanced, very-well-poised, elliptic hypergeometric series.Comment: 21 pages, AMS-LaTe

Essays on the theory of elliptic hypergeometric functions

“…For p → 0, it reduces to the Krattenthaler determinant [88]. Formulae (9.4)-(9.6) are used in [11,34,53,89,90,91] and some other papers as auxiliary tools for proving necessary elliptic hypergeometric identities. Partial fraction decompositions and determinants are somewhat equivalent to each other.…”

An extension of Warnaar’s matrix inversion

“…As was pointed out by Warnaar in [18], his matrix inversion is the elliptic analogue of Krattenthaler's formula. Also, it is worth mentioning that shortly after [18] appeared, Rosengren and Schlosser [14] reproved Warnaar's matrix inversion by using Krattenthaler's operator method.…”

“…Also, it is worth mentioning that shortly after [18] appeared, Rosengren and Schlosser [14] reproved Warnaar's matrix inversion by using Krattenthaler's operator method.…”

“…Recently, as a new class of generalized hypergeometric series originally due to Frenkel and Turaev [5], the elliptic hypergeometric series has received much attention [5,14,17,18]. In [18], Warnaar set up an elliptic matrix inversion by using the addition formula of the theta function [19] and by induction, which proved to be very useful in deriving an extensive list of summation and transformation formulas for elliptic hypergeometric series.…”

“…In [18], Warnaar set up an elliptic matrix inversion by using the addition formula of the theta function [19] and by induction, which proved to be very useful in deriving an extensive list of summation and transformation formulas for elliptic hypergeometric series.…”