On the extended connection coefficients between two orthogonal polynomial sequences

Abstract

In this paper, a concise method to express by induction the so-called extended connection coefficients between two orthogonal polynomial sequences in a general sense is highlighted. Some illustrative examples arising from the semi-classical case are studied.

Keywords:

• orthogonal polynomials
• connection problem
• second-order self-associated polynomials
• semi-classical polynomials

AMS Subject Classification:

• Primary: 33C45
• Secondary: 42C05

Acknowledgements

The author is very grateful to the referee for the constructive and valuable comments and recommendations and for making us pay attention to a certain references.

Disclosure statement

No potential conflict of interest was reported by the author.