The Ramanujan Journal

, Volume 46, Issue 1, pp 29–48 | Cite as

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.

Keywords

Connection coefficients Inversion coefficients Basic hypergeometric polynomials Inverse relations q-Askey scheme d-orthogonal basic polynomials 

Mathematics Subject Classification

33C45 41A10 41A58 

Notes

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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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Higher School of Sciences and TechnologySousse UniversitySousseTunisia

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