Results 11 to 20 of about 2,081 (228)
Generalized degenerate Bernoulli numbers and polynomials arising from Gauss hypergeometric function [PDF]
Advances in Difference Equations, 2021 A new family of p-Bernoulli numbers and polynomials was introduced by Rahmani (J. Number Theory 157:350–366, 2015) with the help of the Gauss hypergeometric function.
Taekyun Kim +4 more
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Several formulas for Bernoulli numbers and polynomials
Advances in Mathematics of Communications, 2023 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Takao Komatsu +2 more
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Degenerate polyexponential functions and type 2 degenerate poly-Bernoulli numbers and polynomials
Advances in Difference Equations, 2020 The polyexponential functions were introduced by Hardy and rediscovered by Kim, as inverses to the polylogarithm functions. Recently, the type 2 poly-Bernoulli numbers and polynomials were defined by means of the polyexponential functions. In this paper,
Taekyun Kim +3 more
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q-Bernoulli numbers and polynomials
Duke Mathematical Journal, 1948 Verf. definiert die \(q\)-Bernoullischen Zahlen \(\beta_m\) durch \(\beta_0=1\), \(\beta_1=-1/(q+1)\) und die symboli\-sche Rekursionsformel \(q(q\beta+1)^m=0\) \((m>1)\), wobei \(\beta^i\) nach Entwicklung durch \(\beta_i\) zu ersetzen ist. Die Zahlen \(\beta_m\) stimmen für \(q=1\) mit den gewöhnlichen Bernoullischen Zahlen überein.
L. Carlitz
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Fully degenerate poly-Bernoulli numbers and polynomials [PDF]
Open Mathematics, 2016 In this paper, we introduce the new fully degenerate poly-Bernoulli numbers and polynomials and inverstigate some properties of these polynomials and numbers.
Kim Taekyun, Kim Dae San, Seo Jong-Jin
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On p-Bernoulli numbers and polynomials
Journal of Number Theory, 2015 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
M. Rahmani
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On generalized q-poly-Bernoulli numbers and polynomials
Filomat, 2020 Many mathematicians in ([1],[2],[5],[14],[20]) introduced and investigated the generalized q-Bernoulli numbers and polynomials and the generalized q-Euler numbers and polynomials and the generalized q-Gennochi numbers and polynomials. Mahmudov ([15],[16]) considered and investigated the q-Bernoulli polynomials B(?)n,q(x,y) in x,y of order ?
Bilgic, Secil, Kurt, Veli
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On hypergeometric Bernoulli numbers and polynomials [PDF]
Acta Mathematica Hungarica, 2017 In this note, we shall provide several properties of hypergeometric Bernoulli numbers and polynomials, including sums of products identity, differential equations and recurrence formulas.
Hu, S., Kim, M.-S.
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A new approach to fully degenerate Bernoulli numbers and polynomials [PDF]
Filomat, 2022 In this paper, we consider the doubly indexed sequence a(r) ? (n,m), (n,m ? 0), defined by a recurrence relation and an initial sequence a(r) ? (0,m), (m ? 0). We derive with the help of some differential operator an explicit expression for a(r) ? (n,
Taekyun Kim, Dae San Kim
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A note on degenerate multi-poly-Bernoulli numbers and polynomials [PDF]
Applicable Analysis and Discrete Mathematics, 2020 In this paper, we consider the degenerate multi-poly-Bernoulli numbers and polynomials which are defined by means of the multiple polylogarithms and degenerate versions of the multi-poly-Bernoulli numbers and polynomials.
Taekyun Kim, Dae San Kim
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