On structure formulas for Wilson polynomials

Abstract

By studying various properties of some divided difference operators, we prove that Wilson polynomials are solutions of a second-order difference equation of hypergeometric type. Next, some new structure relations are deduced, the inversion and the connection problems are solved using an algorithmic method.

Keywords:

• Wilson polynomials
• quadratic lattices
• difference equations
• hypergeometric representation
• structure relation
• inversion formula
• connection coefficients

AMS Subject Classification:

• 33C20
• 33C25
• 42C05

Acknowledgements

We would like to thank the anonymous reviewer of this paper for very carefully reading the manuscript, and also for his valuable comments and suggestions which improved the paper significantly.

Disclosure statement

No potential conflict of interest was reported by the authors.

Funding

This work has been partially supported by the STIBET fellowship of DAAD for P. Njionou Sadjang, the Institute of Mathematics of the University of Kassel (Germany), the 2014–2015 Research Grant of AIMS-Cameroon and a Research-Group Linkage Programme 2009–2012 between the University of Kassel (Germany) and the University of Yaounde I (Cameroon) sponsored by the Alexander von Humboldt Foundation. All these institutions receive our sincere thanks.