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Connection and inversion coefficients for basic hypergeometric polynomials

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Abstract

In this paper, we give a closed-form expression of the inversion and the connection coefficients for general basic hypergeometric polynomial sets using some known inverse relations. We derive expansion formulas corresponding to all the families within the q-Askey scheme and we connect some d-orthogonal basic hypergeometric polynomials.

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Acknowledgements

Sincere thanks are due to the referee for his/her careful reading of the manuscript and for his/her valuable comments and suggestions which have considerably improved the quality of this paper.

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Authors and Affiliations

  1. Higher School of Sciences and Technology, Sousse University, Sousse, Tunisia

    Hamza Chaggara & Mohamed Mabrouk

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  1. Hamza Chaggara
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  2. Mohamed Mabrouk
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Correspondence to Hamza Chaggara.

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Dedicated to Professor Tom Koornwinder

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Chaggara, H., Mabrouk, M. Connection and inversion coefficients for basic hypergeometric polynomials. Ramanujan J 46, 29–48 (2018). https://doi.org/10.1007/s11139-017-9951-0

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