• Title, Summary, Keyword: degenerate Bernoulli polynomials

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DEGENERATE BERNOULLI NUMBERS AND POLYNOMIALS ASSOCIATED WITH DEGENERATE HERMITE POLYNOMIALS

  • Haroon, Hiba;Khan, Waseem Ahmad
    • Communications of the Korean Mathematical Society
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    • v.33 no.2
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    • pp.651-669
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    • 2018
  • The article is themed to classify new (fully) degenerate Hermite-Bernoulli polynomials with formulation in terms of p-adic fermionic integrals on $\mathbb{Z}_p$. The entire paper is designed to illustrate new properties in association with Daehee polynomials in a consolidated and generalized form.

SYMMETRIC IDENTITIES FOR DEGENERATE q-POLY-BERNOULLI NUMBERS AND POLYNOMIALS

  • JUNG, N.S.;RYOO, C.S.
    • Journal of applied mathematics & informatics
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    • v.36 no.1_2
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    • pp.29-38
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    • 2018
  • In this paper, we introduce a degenerate q-poly-Bernoulli numbers and polynomials include q-logarithm function. We derive some relations with this polynomials and the Stirling numbers of second kind and investigate some symmetric identities using special functions that are involving this polynomials.

ON FINITE TIMES DEGENERATE HIGHER-ORDER CAUCHY NUMBERS AND POLYNOMIALS

  • Jeong, Joohee;Rim, Seog-Hoon
    • Bulletin of the Korean Mathematical Society
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    • v.53 no.5
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    • pp.1427-1437
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    • 2016
  • Cauchy polynomials are also called Bernoulli polynomials of the second kind and these polynomials are very important to study mathematical physics. D. S. Kim et al. have studied some properties of Bernoulli polynomials of the second kind associated with special polynomials arising from umbral calculus. T. Kim introduced the degenerate Cauchy numbers and polynomials which are derived from the degenerate function $e^t$. Recently J. Jeong, S. H. Rim and B. M. Kim studied on finite times degenerate Cauchy numbers and polynomials. In this paper we consider finite times degenerate higher-order Cauchy numbers and polynomials, and give some identities and properties of these polynomials.

ON p-ADIC INTEGRAL FOR GENERALIZED DEGENERATE HERMITE-BERNOULLI POLYNOMIALS ATTACHED TO χ OF HIGHER ORDER

  • Khan, Waseem Ahmad;Haroon, Hiba
    • Honam Mathematical Journal
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    • v.41 no.1
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    • pp.117-133
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    • 2019
  • In the current investigation, we obtain the generating function for Hermite-based degenerate Bernoulli polynomials attached to ${\chi}$ of higher order using p-adic methods over the ring of integers. Useful identities, formulae and relations with well known families of polynomials and numbers including the Bernoulli numbers, Daehee numbers and the Stirling numbers are established. We also give identities of symmetry and additive property for Hermite-based generalized degenerate Bernoulli polynomials attached to ${\chi}$ of higher order. Results are supported by remarks and corollaries.

A FURTHER INVESTIGATION OF GENERATING FUNCTIONS RELATED TO PAIRS OF INVERSE FUNCTIONS WITH APPLICATIONS TO GENERALIZED DEGENERATE BERNOULLI POLYNOMIALS

  • Gaboury, Sebastien;Tremblay, Richard
    • Bulletin of the Korean Mathematical Society
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    • v.51 no.3
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    • pp.831-845
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    • 2014
  • In this paper, we obtain new generating functions involving families of pairs of inverse functions by using a generalization of the Srivastava's theorem [H. M. Srivastava, Some generalizations of Carlitz's theorem, Pacific J. Math. 85 (1979), 471-477] obtained by Tremblay and Fug$\grave{e}$ere [Generating functions related to pairs of inverse functions, Transform methods and special functions, Varna '96, Bulgarian Acad. Sci., Sofia (1998), 484-495]. Special cases are given. These can be seen as generalizations of the generalized Bernoulli polynomials and the generalized degenerate Bernoulli polynomials.