New $q$-identities Via $q$-Derivative of Basic Hypergeometric Series with Respect to Parameters
Ronald Orozco L\'opez
TL;DR
This paper derives new $q$-identities by applying $q$-differential and deformed $q$-exponential operators to basic hypergeometric series, expanding the theoretical framework of $q$-series transformations.
Contribution
It introduces novel $q$-identities obtained through $q$-derivative techniques applied to classical hypergeometric sums and transformations.
Findings
New $q$-identities derived from $q$-Gauss sum
Extensions of $q$-Chu-Vandermonde's sum
Transformations of Jackson's formula
Abstract
In this paper, we use the effect of the -differential and deformed -exponential operators on basic hypergeometric series to find new -identities from the -Gauss sum, the -Chu-Vandermonde's sum, and Jackson's transformation formula.
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Taxonomy
TopicsAdvanced Mathematical Identities · Mathematical functions and polynomials · Algebraic structures and combinatorial models