A FINITE SUM INVOLVING GENERALIZED FALLING FACTORIAL POLYNOMIALS AND DEGENERATE EULERIAN POLYNOMIALS

Taekyun Kim (), Dae San Kim (), Jin-Woo Park and Salah Mahmoud Boulaaras ()
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Taekyun Kim: Department of Mathematics, Kwangwoon University, Seoul 139-701, Republic of Korea
Dae San Kim: Department of Mathematics, Sogang University, Seoul 121-742, Republic of Korea
Jin-Woo Park: Department of Mathematics Education, Daegu University, Daegu, Republic of Korea
Salah Mahmoud Boulaaras: Department of Mathematics, College of Science and Arts, Qassim University, Alras City, Qassim, Saudi Arabia

FRACTALS (fractals), 2022, vol. 30, issue 10, 1-9

Abstract: The aim of this paper is two-fold. First, we investigate a finite sum involving the generalized falling factorial polynomials, in some special cases of which we express it in terms of the degenerate Stirling numbers of the second kind, the degenerate Bernoulli polynomials and the degenerate Frobenius–Euler polynomials. Second, we consider the degenerate Eulerian polynomials and deduce the generating function and a recurrence relation for them.

Keywords: Degenerate Stirling Numbers of the Second Kind; Degenerate Exponentials; Degenerate Frobenius–Euler Polynomials; Degenerate Eulerian Numbers and Polynomials; Unsigned Degenerate Stirling Numbers of the First Kind (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22401910

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