Some identities of degenerate higher-order Daehee polynomials based on (Formula presented)-umbral calculus

Dojin Kim, Sangbeom Park, Jongkyum Kwon

Research output: Contribution to journalArticlepeer-review

Abstract

The degenerate versions of special polynomials and numbers, initiated by Carlitz, have regained the attention of some mathematicians by replacing the usual exponential function in the generating function of special polynomials with the degenerate exponential function. To study the relations between degenerate special polynomials, (Formula presented)-umbral calculus, an analogue of umbral calculus, is intensively applied to obtain related formulas for expressing one (Formula presented)-Sheffer polynomial in terms of other (Formula presented)-Sheffer polynomials. In this paper, we study the connection between degenerate higher-order Daehee polynomials and other degenerate type of special polynomials. We present explicit formulas for representations of the polynomials using (Formula presented)-umbral calculus and confirm the presented formulas between the degenerate higher-order Daehee polynomials and the degenerate Bernoulli polynomials, for example. Additionally, we investigate the pattern of the root distribution of these polynomials.

Original languageEnglish
Pages (from-to)3064-3085
Number of pages22
JournalElectronic Research Archive
Volume31
Issue number6
DOIs
StatePublished - 2023

Keywords

  • (Formula presented)-Sheffer polynomial
  • (Formula presented)-umbral calculus
  • degenerate higher-order Daehee polynomial
  • generating function
  • special polynomial

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