Higher order recurrence relation for exceptional Charlier, Meixner, Hermite and Laguerre orthogonal polynomials

Abstract

In this paper we prove in a constructing way that exceptional Charlier, Meixner, Hermite and Laguerre polynomials satisfy higher order recurrence relations. Our conjecture is that the recurrence relations provided in this paper have minimal order.

Keywords:

• orthogonal polynomials
• exceptional orthogonal polynomial
• recurrence relations
• difference operators
• differential operators
• Charlier polynomials
• Meixner polynomials
• Hermite polynomials
• Laguerre polynomials

1991 Mathematics Subject Classification::

• 42C05
• 33C45
• 33E30

Disclosure statement

No potential conflict of interest was reported by the author.

Funding

Partially supported by MTM2012-36732-C03-03 (Ministerio de Economía y Competitividad), FQM-262, FQM-4643, FQM-7276 (Junta de Andalucía) and Feder Funds (European Union).