Connection and inversion coefficients for basic hypergeometric polynomials
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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.
KeywordsConnection coefficients Inversion coefficients Basic hypergeometric polynomials Inverse relations q-Askey scheme d-orthogonal basic polynomials
Mathematics Subject Classification33C45 41A10 41A58
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.