The single-indexed exceptional Krawtchouk polynomials
Hiroshi Miki, Satoshi Tsujimoto, Luc Vinet
TL;DR
This paper explores the Darboux transformations of Krawtchouk polynomials, focusing on exceptional variants derived from single-step transformations, and investigates their properties including Diophantine equations and recurrence relations.
Contribution
It provides a comprehensive analysis of all single-step Darboux-derived exceptional Krawtchouk polynomials and their mathematical properties.
Findings
Characterization of all single-step Darboux-derived exceptional Krawtchouk polynomials
Derivation of recurrence relations for these polynomials
Identification of Diophantine properties associated with the 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.
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Taxonomy
TopicsNonlinear Waves and Solitons · Molecular spectroscopy and chirality · Advanced Mathematical Theories and Applications