On certain q-hypergeometric matrix functions of several variables and their matrix q-difference equations

ABSTRACT

We introduce q-Lauricella matrix functions of three and n-variables. The convergence of these matrix functions is examined for both $|q|<1$ and $|q|>1$ cases. The systems of matrix q-difference equations satisfied by these q-Lauricella matrix functions as well as basic Srivastava's triple hypergeometric matrix functions have been determined. Certain integral representations satisfied by these matrix functions have also been established.

KEYWORDS:

• q-hypergeometric function
• q-Lauricella functions
• matrix functional calculus

AMS SUBJECT CLASSIFICATIONS:

• 15A15
• 33D15
• 33D70

Acknowledgements

The authors thank the referees for valuable suggestions that led to a better presentation of the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Vivek Sahai http://orcid.org/0000-0002-7527-5346

Additional information

Funding

The financial assistance provided to the first author in the form of a Senior Research Fellowship from Council of Scientific and Industrial Research, India is gratefully acknowledged.