Results 1 to 10 of about 18,284 (134)
Explicit Formulas Involving -Euler Numbers and Polynomials [PDF]
Abstract and Applied Analysis, 2012 We deal with -Euler numbers and -Bernoulli numbers. We derive some interesting relations for -Euler numbers and polynomials by using their generating function and derivative operator.
Serkan Araci +2 more
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Advances in Difference Equations, 2021 Recently, Kim et al. (Adv. Differ. Equ. 2020:168, 2020) considered the poly-Bernoulli numbers and polynomials resulting from the moderated version of degenerate polyexponential functions. In this paper, we investigate the degenerate type 2 poly-Bernoulli
Waseem A. Khan +3 more
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Fully degenerate Bernoulli numbers and polynomials
Demonstratio Mathematica, 2022 The aim of this article is to study the fully degenerate Bernoulli polynomials and numbers, which are a degenerate version of Bernoulli polynomials and numbers and arise naturally from the Volkenborn integral of the degenerate exponential functions on Zp{
Kim Taekyun, Kim Dae San, Park Jin-Woo
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Some Identities of the Degenerate Multi-Poly-Bernoulli Polynomials of Complex Variable
Journal of Function Spaces, 2021 In this paper, we introduce degenerate multi-poly-Bernoulli polynomials and derive some identities of these polynomials. We give some relationship between degenerate multi-poly-Bernoulli polynomials degenerate Whitney numbers and Stirling numbers of the ...
G. Muhiuddin +3 more
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Bernoulli F-polynomials and Fibo–Bernoulli matrices
Advances in Difference Equations, 2019 In this article, we define the Euler–Fibonacci numbers, polynomials and their exponential generating function. Several relations are established involving the Bernoulli F-polynomials, the Euler–Fibonacci numbers and the Euler–Fibonacci polynomials. A new
Semra Kuş, Naim Tuglu, Taekyun Kim
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A Parametric Type of Cauchy Polynomials with Higher Level
Axioms, 2021 There are many kinds of generalizations of Cauchy numbers and polynomials. Recently, a parametric type of the Bernoulli numbers with level 3 was introduced and studied as a kind of generalization of Bernoulli polynomials.
Takao Komatsu
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The Zagier polynomials. Part II: Arithmetic properties of coefficients [PDF]
, 2013 The modified Bernoulli numbers \begin{equation*} B_{n}^{*} = \sum_{r=0}^{n} \binom{n+r}{2r} \frac{B_{r}}{n+r}, \quad n > 0 \end{equation*} introduced by D. Zagier in 1998 were recently extended to the polynomial case by replacing $B_{r}$ by the Bernoulli
Coffey, Mark W. +5 more
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Generalized degenerate Bernoulli numbers and polynomials arising from Gauss hypergeometric function
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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Mathematics, 2021 In this paper, we further study the generating function involving a variety of special numbers and ploynomials constructed by the second author. Applying the Mellin transformation to this generating function, we define a new class of zeta type functions,
Daeyeoul Kim, Yilmaz Simsek
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Advances in Difference Equations, 2019 In recent years, studying degenerate versions of various special polynomials and numbers has attracted many mathematicians. Here we introduce degenerate type 2 Bernoulli polynomials, fully degenerate type 2 Bernoulli polynomials, and degenerate type 2 ...
Dae San Kim +3 more
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