<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In this article, we first introduce and study a new family of the multi-index and multi-variable Gould-Hopper and Dattoli type polynomials {<italic>Hn<sup>(cm, cm-1,…, c3, c2)</sup>(a1, a2, …, am</italic>} defined by (2.1), which are an extension of different types of Her-mite polynomials defined in section 1. We next consider multi-variable linear, bilinear and bilateral generating relations of the newly defined hypergeometric polynomials, using series iteration techniques. Further, we generalize these generating relations in the forms of multiple series identities involving bounded multiple sequences, Fox-Wright hypergeometric function and Srivastava-Daoust multi-variable hypergeometric function.</p></abstract>

In this article, we first introduce and study a new family of the multi-index and multi-variable Gould-Hopper and Dattoli type polynomials {Hn(cm, cm-1,…, c3, c2)(a1, a2, …, am} defined by (2.1), which are an extension of different types of Her-mite polynomials defined in section 1. We next consider multi-variable linear, bilinear and bilateral generating relations of the newly defined hypergeometric polynomials, using series iteration techniques. Further, we generalize these generating relations in the forms of multiple series identities involving bounded multiple sequences, Fox-Wright hypergeometric function and Srivastava-Daoust multi-variable hypergeometric function.

Some Srivastava-Brafman Type Generating Relations For A General Class Of Multi-Index And Multi-Variable Gould-Hopper And Dattoli Type Hypergeometric Polynomials

Department of Applied Sciences and Humanities, Faculty of Engineering and Technology, Jamia Millia Islamia (A Central University), New Delhi-110025 (India)

Mathematics Section, Mewat Engineering College (Waqf), Palla, Nuh, Mewat-122107, Haryana (India)

Department of Applied Sciences and Humanities, Aryabhat Polytechnic, G. T. Karnal Road, Delhi-110033 (India)

Journal of Applied Mathematics, Statistics and Informatics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

In this article, we first introduce and study a new family of the multi-index and multi-variable Gould-Hopper and Dattoli type polynomials {Hn(cm, cm-1,…, c3,...

Some Srivastava-Brafman Type Generating Relations For A General Class Of Multi-Index And Multi-Variable Gould-Hopper And Dattoli Type Hypergeometric Polynomials

Published Online: Jul 15, 2014

Page range: 31 - 44

DOI: https://doi.org/10.2478/jamsi-2014-0003

© 2014 Faculty of Natural Sciences, University of Saint Cyril and Metodius

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.