Hypergeometric solutions for variants of the $q$-hypergeometric equation
Taikei Fujii, Takahiko Nobukawa
TL;DR
This paper characterizes variants of the $q$-hypergeometric equation using configurations, providing integral and series solutions, and enhances understanding of $q$-difference equations in mathematical analysis.
Contribution
It introduces a configuration-based characterization of $q$-hypergeometric variants and constructs explicit integral and series solutions for them.
Findings
Characterization of $q$-hypergeometric variants via configurations
Explicit integral solutions for the variants
Series solutions for the variants
Abstract
We introduce a configuration of a -difference equation and characterize the variants of the -hypergeometric equation, which were defined by Hatano-Matsunawa-Sato-Takemura, by configurations. We show integral solutions and series solutions for the variants of the -hypergeometric equation.
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Taxonomy
TopicsPolynomial and algebraic computation · Nonlinear Waves and Solitons · Advanced Mathematical Identities