Two finite hypergeometric sequences of discrete orthogonal polynomials

ABSTRACT

Two finite hypergeometric sequences of symmetric orthogonal polynomials of a discrete variable are introduced and their standard properties, such as second-order difference equations, explicit forms of the polynomials and three term recurrence relations are obtained. As a consequence of two specific Sturm–Liouville problems, it is proved that these polynomials are finitely orthogonal with respect to two symmetric weight functions.

KEYWORDS:

• Extended Sturm–Liouville theorem for symmetric functions of a discrete variable
• orthogonal polynomials of a discrete variable
• hypergeometric series
• norm square value
• moments

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• Primary: 42C05
• 33E30
• 33C47
• Secondary: 33C45
• 33C20

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work has been supported by a grant from ‘Alexander von Humboldt-Stiftung Foundation’ No. Ref 3.4 – IRN – 1128637 – GF-E.