The single-indexed exceptional Krawtchouk polynomials

ABSTRACT

The Darboux transformations of Krawtchouk polynomials are investigated and all possible exceptional Krawtchouk polynomials obtainable from a single-step Darboux transformation are considered. The properties of these exceptional Krawtchouk polynomials including the Diophantine ones and the recurrence relations are obtained.

KEYWORDS:

• Krawtchouk polynomials
• exceptional krawtchouk polynomials
• orthogonal polynomials
• diophantine property
• recurrence relations

MATHEMATICS SUBJECT CLASSIFICATION:

• 33C45

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The research of HM and ST is supported by JSPS KAKENHI [grant numbers 22H04197 and 19H01792], respectively, and that of LV by a discovery grant of the Natural Sciences and Engineering Research Council (NSERC) of Canada.