On combinatorial properties of the degenerate Krawtchouk Appell polynomials

Mohamed Abdelkader; Mohamed Rhaima; Mohamed Abdelkader; Mohamed Rhaima

doi:10.3934/math.2026831

AIMS Mathematics

2026, Volume 11, Issue 7: 20440-20460. doi: 10.3934/math.2026831

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Research article

On combinatorial properties of the degenerate Krawtchouk Appell polynomials

Mohamed Abdelkader ^,,
Mohamed Rhaima

Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia

Received: 19 April 2026 Revised: 15 June 2026 Accepted: 23 June 2026 Published: 13 July 2026
MSC : 33C45, 11C08, 94A11, 42C05, 94A11

The foremost aim of this study is to introduce and study several combinatorial properties and highlight specific aspects of a new class of polynomial sequences, known as degenerate Krawtchouk Appell polynomials, associated with the degenerate Pascal measure. As an application, the connection between these brand-new polynomials, Stirling numbers, the scaling operator, the translation operator, and orthogonal Bell polynomials have been investigated.
- Bell polynomials,
- degenerate Pascal measure,
- degenerate Krawtchouk Appell polynomials,
- scaling operator
Citation: Mohamed Abdelkader, Mohamed Rhaima. On combinatorial properties of the degenerate Krawtchouk Appell polynomials[J]. AIMS Mathematics, 2026, 11(7): 20440-20460. doi: 10.3934/math.2026831

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Abstract

The foremost aim of this study is to introduce and study several combinatorial properties and highlight specific aspects of a new class of polynomial sequences, known as degenerate Krawtchouk Appell polynomials, associated with the degenerate Pascal measure. As an application, the connection between these brand-new polynomials, Stirling numbers, the scaling operator, the translation operator, and orthogonal Bell polynomials have been investigated.

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