Results 81 to 90 of about 146,038 (187)
Probabilistic degenerate Bernoulli and degenerate Euler polynomials
Mathematical and Computer Modelling of Dynamical SystemsRecently, many authors have studied degenerate Bernoulli and degenerate Euler polynomials. Let [Formula: see text] be a random variable whose moment generating function exists in a neighbourhood of the origin.
Lingling Luo +3 more
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Generalizations of the Bernoulli and Appell polynomials
Abstract and Applied Analysis, 2004 We first introduce a generalization of the Bernoulli polynomials, and consequently of the Bernoulli numbers, starting from suitable generating functions related to a class of Mittag-Leffler functions.
Gabriella Bretti +2 more
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A note on type 2 q-Bernoulli and type 2 q-Euler polynomials
Journal of Inequalities and Applications, 2019 As is well known, power sums of consecutive nonnegative integers can be expressed in terms of Bernoulli polynomials. Also, it is well known that alternating power sums of consecutive nonnegative integers can be represented by Euler polynomials.
Dae San Kim +3 more
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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.
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Convolution Identities for Bernoulli and Genocchi Polynomials [PDF]
The Electronic Journal of Combinatorics, 2014 The main purpose of this paper is to derive various Matiyasevich-Miki-Gessel type convolution identities for Bernoulli and Genocchi polynomials and numbers by applying some Euler type identities with two parameters.
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Congruences involving Bernoulli polynomials
Discrete Mathematics, 2008 The author proves congruences modulo \(p\), an odd prime, between values of Bernoulli polynomials \(B_n(x)\) and certain sums of Kronecker symbols \(({k\over p})\) or, alternatively, sums of binomial coefficients \(p\choose k\). He also proves similar congruences for Euler polynomials \(E_n(x)\).
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Duals of the Bernoulli Numbers and Polynomials and the Euler Numbers and Polynomials
Integers, 2017 See the abstract in the attached pdf.
Tian-Xiao He, Jinze Zheng
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A New Approach to
Advances in Difference Equations, 2010 We present a new generating function related to the -Bernoulli numbers and -Bernoulli polynomials. We give a new construction of these numbers and polynomials related to the second-kind Stirling numbers and -Bernstein polynomials.
Açikgöz Mehmet +2 more
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POLYLOGARITHMS AND POLY-BERNOULLI POLYNOMIALS
In this paper we investigate special generalized Bernoulli polynomials that generalize classical Bernoulli polynomials and numbers. We call them poly-Bernoulli polynomials. We prove a collection of extremely important and fundamental identities satisfied
Hamahata, Yoshinori +3 more
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On the 𝑞-Bernoulli Numbers and Polynomials with Weight 𝜶
Abstract and Applied Analysis, 2011 We present a systemic study of some families of higher-order 𝑞-Bernoulli numbers and polynomials with weight 𝛼. From these studies, we derive some interesting identities on the 𝑞-Bernoulli numbers and polynomials with weight 𝛼.
T. Kim, J. Choi
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