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Some Identities Of Fully Degenerate Dowling And Fully Degenerate Bell Polynomials Arising From λ-Umbral Calculus

Author

Listed:
  • YUANKUI MA

    (School of Science, Xi’an Technological University, Xi’an, Shaanxi, 710021, P. R. China)

  • TAEKYUN KIM

    (School of Science, Xi’an Technological University, Xi’an, Shaanxi, 710021, P. R. China†Department of Mathematics, Kwangwoon University, Seoul 139-701, Republic of Korea)

  • HYUNSEOK LEE

    (��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)

Abstract

Recently, Kim–Kim introduced the λ-umbral calculus, in which the λ-Sheffer sequences occupy the central position. In this paper, we introduce the fully degenerate Bell and the fully degenerate Dowling polynomials, and investigate some properties and identities relating to those polynomials with the help of λ-umbral calculus. Here, we note that the fully degenerate Bell poynomials and the fully degenerate Dowling polynomials are, respectively, degenerate versions of the Bell polynomials and the Dowling polynomials, of which the latters are the natural extension of the Whitney numbers of the second kind.

Suggested Citation

  • Yuankui Ma & Taekyun Kim & Hyunseok Lee & Dae San Kim, 2022. "Some Identities Of Fully Degenerate Dowling And Fully Degenerate Bell Polynomials Arising From λ-Umbral Calculus," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(10), pages 1-10, December.
    • Handle: RePEc:wsi:fracta:v:30:y:2022:i:10:n:s0218348x22402575
    DOI: 10.1142/S0218348X22402575
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