Limits of elliptic hypergeometric integrals
Eric M. Rains
Abstract
In math.QA/0309252, the author proved a number of multivariate elliptic hypergeometric integrals. The purpose of the present note is to explore more carefully the various limiting cases (hyperbolic, trigonometric, rational, and classical) that exist. In particular, we show (using some new estimates of generalized gamma functions) that the hyperbolic integrals (previously treated as purely formal limits) are indeed limiting cases. We also obtain a number of new trigonometric (q-hypergeometric) integral identities as limits from the elliptic level.
Create a lesson
Related papers
The Erdélyi--Magnus--Nevai and Krasikov Conjectures for Jacobi Polynomials
Qi-Feng Bai, Yu-Tian Li
A Painlevé equation for the Hörmander-Bernhardsson constant
Friedrich Littmann
Square Functions and Rectifiability under Monotone Transformations of the Density
Triet M. Le
On the Coefficients of Hurwitz-Type Matrix Polynomials
Abdon E. Choque-Rivero
Counterexamples for generalizations of the non-elliptic Schrödinger maximal operator
Rena Chu
Monodromy and Isomonodromy for Linear q-Difference Systems with Coefficient Matrix Ax+B
Jinghong Lin, Qian Tang, Xiaomeng Xu