q-derivatives of multivariable q-hypergeometric function with respect to their parameters

TL;DR

This paper investigates the q-derivatives of multivariable hypergeometric functions, providing explicit formulas and examples, enhancing understanding of their parameter sensitivities in the context of q-series.

Contribution

It introduces explicit formulas for q-derivatives of multivariable hypergeometric functions with respect to parameters, including specific derivatives of the q-analog of Horn type functions.

Findings

Explicit equations for q-derivatives with positive real coefficients

Derivatives of q-analog of Horn type hypergeometric function H_3 provided

Enhanced understanding of parameter dependence in multivariable q-hypergeometric functions

Abstract

We consider the q-derivatives of the Srivastava and Daoust basic multivariable hypergeometric function with respect to the parameters. This function embodies a entire number of various q-hypergeometric series of one and several variables. Explicit equations are given for general case of summation indexes with positive real coefficients. As an example derivatives of q-analog of non-confluent Horn type hypergeometric function $H_3$ is presented.