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.
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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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Dave, B.I. A general q-inverse series relation. Bol. Soc. Mat. Mex. 24, 279–299 (2018). https://doi.org/10.1007/s40590-017-0172-8
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DOI: https://doi.org/10.1007/s40590-017-0172-8
Keywords
- Riordan’s inverse pairs
- series orthogonality
- q-Racah polynomial
- Askey–Wilson polynomials
- q-Neumann expansion