Some expansion formulas for Brenke polynomial sets

Abstract

In this paper, using operational rules, we derive some explicit expansion formulas associated with Brenke type polynomials. In particular, the corresponding connection and linearization coefficients are expressed either in terms of double sums or integral representations or sometimes in closed hypergeometric terms. The derived results are applied to Generalized Gould–Hopper and q-Laguerre polynomials. Some well-known duplication and convolution formulas are deduced as particular cases.

Keywords:

• Connection coefficients
• linearization coefficients
• generating functions
• Brenke polynomials
• generalized Gould–Hopper polynomials
• q-Laguerre polynomials

2010 Mathematics Subject classifications:

• 33C45
• 39A70
• 41A10
• 41A58

Acknowledgements

The authors thank the referees for their careful reading of the manuscript and for their constructive comments and suggestions. The first author, Hamza Chaggara, would like to extend his appreciation to the Deanship of Scientific Research at King Khalid University for funding this work through Small Groups. Project under grant number (RGP1/141/44).

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

Data sharing not applicable to this article as no data sets were generated or analyzed during the current study.

Additional information

Funding

This work was funded by the Deanship of Scientific Research at King Khalid University through the Small Group Research Project (grant number: RGP1/141/44).