Symmetry Techniques and Generating Functions for Basic Analogue of Fox's H-Function

The objective of this paper is to establish the q-recurrence relations, q-difference equations for basic analogue of Fox's H-function and then obtain the canonical equation associated with each family of multivariable q-analogue of Fox's H-function and generating functions of families of basic analogue of  Fox's H-function. A significantly large number of works on the subject of H- function gives interesting account of the theory and its applications in many different areas of mathematical analysis. A lot of research work has been recently come up on the study and development of a function that is more general.