Jackson integral representation for a multiple q-hypergeometric series and an extension of the q-Riemann-Papperitz system

2024/02/22 by Nobukawa, Takahiko
#33D60 #33D70 #39A13 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2402.14358

Abstract

We give a Jackson integral representation for Kajihara's q-hypergeometric series W^M,2. We construct a q-difference system that corresponds to this integral. This system is an extension of the variant of q-hypergeometric equation of degree three, defined by Hatano-Matsunawa-Sato-Takemura. We show that this system includes the q-Appell-Lauricella system as a degeneration.

Related

• Connection formula for the Jackson integral of Riemann-Papperitz type
• Hypergeometric solutions for variants of the q-hypergeometric equation
• Solutions to variant of q-hypergeometric equation of degree 2 associated with q-middle convolution
• Generalized hypergeometric functions with several variables
• Jackson Integral Representations of Modified q-Bessel Functions and q-Bessel-Macdonald Functions