Multidimensional Extensions of Basic (or q-)Analogs of Certain Erdélyi Type Integrals

A number of Erdélyi-type integrals for certain hypergeometric functions with their multidimensional extensions have been studied in the literature. The basic (or q-) analogs of such integrals have also been analyzed but the multidimensional extensions of basic (or q-) analogs of these integrals have not appeared so far. This work aims to develop multidimensional extensions of certain Erdélyi-type \(q\) -integrals. The motivation behind this work stems from the recognition that basic (or q-) gamma and q-hypergeometric functions, and q-integrals, hold significant relevance across various domains. Their applications extend to diverse fields including Number Theory, Partitions, Combinatorics, Physics, and exploring q-deformed systems in Nonlinear Dynamics.