A general q-inverse series relation

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Abstract

In the present work, we establish a general inverse series relations which unify the polynomials of Askey–Wilson, q-Racah, and q-Konhauser. The q-extensions of Riordan’s inverse series relations [Combinatorial Identities, John Wiley and Sons, Inc. 1968] are obtained by means of the main two theorems. Then we emphasize on the special cases, namely the q-Bessel function together with a q-Neumann expansion, and an inverse pair associated with the partition identities.

Keywords

Riordan’s inverse pairs series orthogonality q-Racah polynomial Askey–Wilson polynomials q-Neumann expansion 

Mathematics Subject Classification

5A19 11B65 33D65 33D99 
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Notes

Acknowledgements

The author is indebted to his guide Prof. J.P. Singhal for his encouragement; and thankful to Ms. Reshma T. Shah (Asst. Professor, CHARUSET, Changa), and the Research scholar Ms. Meera Chudasama for their kind assistance in LaTeXtype-setting. The author also expresses his sincere thanks to the referee(s) for the improvement of the manuscript.

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Copyright information

© Sociedad Matemática Mexicana 2017

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of ScienceThe Maharaja Sayajirao University of BarodaVadodaraIndia

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