Nonterminating transformations and summations associated with some q-Mellin--Barnes integrals

2022/06/10 by Cohl, Howard S., Costas-Santos, Roberto S. · 1 citation
#33D15 #33D60 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2206.05222

Abstract

In many cases one may encounter an integral which is of q-Mellin--Barnes type. These integrals are easily evaluated using theorems which have a long history dating back to Slater, Askey, Gasper, Rahman and others. We derive some interesting q-Mellin--Barnes integrals and using them we derive transformation and summation formulas for nonterminating basic hypergeometric functions. The cases which we treat include ratios of theta functions, the Askey--Wilson moments, nonterminating well-poised ₃ϕ₂, nonterminating very-well-poised ₅W₄, ₈W₇, products of two nonterminating ₂ϕ₁'s, square of a nonterminating well-poised ₂ϕ₁, and nonterminating ₁₂W₁₁ and ₁₀W₉.

Cited by

• Residue sums for superconformal indices

Related

• Nonterminating Basic Hypergeometric Series and the q-Zeilberger Algorithm
• Euler--Mellin integrals and A-hypergeometric functions
• Mellin-Barnes integrals as Fourier-Mukai transforms
• Mellin transforms with only critical zeros: Legendre functions
• Product formulas for basic hypergeometric series by evaluations of Askey--Wilson polynomials