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A Finite Sum Involving Generalized Falling Factorial Polynomials And Degenerate Eulerian Polynomials

Author

Listed:
  • 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)

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.

Suggested Citation

  • Taekyun Kim & Dae San Kim & Jin-Woo Park & Salah Mahmoud Boulaaras, 2022. "A Finite Sum Involving Generalized Falling Factorial Polynomials And Degenerate Eulerian Polynomials," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(10), pages 1-9, December.
    • Handle: RePEc:wsi:fracta:v:30:y:2022:i:10:n:s0218348x22401910
    DOI: 10.1142/S0218348X22401910
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