Results 21 to 30 of about 15,530 (193)
An Extended Generalized q-Extensions for the Apostol Type Polynomials
Abstract and Applied Analysis, 2018 Through a modification on the parameters associated with generating function of the q-extensions for the Apostol type polynomials of order α and level m, we obtain some new results related to a unified presentation of the q-analog of the generalized ...
Letelier Castilla +2 more
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Axioms, 2021 In this article, we derive representation formulas for a class of r-associated Stirling numbers of the second kind and examine their connections with a class of generalized Bernoulli polynomials.
Paolo Emilio Ricci +2 more
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Generalised Bernoulli polynomials and series [PDF]
Bulletin of the Australian Mathematical Society, 2000 We present several results related to the recently introduced generalised Bernoulli polynomials. Some recurrence relations are given, which permit us to compute efficiently the polynomials in question. The sums , where jk = jk (α) are the zeros of the Bessel function of the first kind of order α, are evaluated in terms of these polynomials.
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Some Identities of Symmetry for the Generalized Bernoulli Numbers and Polynomials
Abstract and Applied Analysis, 2009 By the properties of p-adic invariant integral on ℤp, we establish various identities concerning the generalized Bernoulli numbers and polynomials. From the symmetric properties of p-adic invariant integral on ℤp, we give some interesting relationship ...
Taekyun Kim, Seog-Hoon Rim, Byungje Lee
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A Note on Bernoulli Numbers and Shintani Generalized Bernoulli Polynomials [PDF]
Transactions of the American Mathematical Society, 1996 Generalized Bernoulli polynomials were introduced by Shintani in 1976 in order to express the special values at non-positive integers of Dedekind zeta functions for totally real numbers. The coefficients of such polynomials are finite combinations of products of Bernoulli numbers which are difficult to get hold of. On the other hand, Zagier was able to
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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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New results on the q-generalized Bernoulli polynomials of level m
Demonstratio Mathematica, 2019 This paper aims to show new algebraic properties from the q-generalized Bernoulli polynomials Bn[m-1](x;q)B_n^{[m - 1]}(x;q) of level m, as well as some others identities which connect this polynomial class with the q-generalized Bernoulli polynomials of
Urieles Alejandro +3 more
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Sums of products of generalized Bernoulli polynomials [PDF]
Pacific Journal of Mathematics, 2003 The author investigates the zeta function \[ Z(P,\chi,a,s)= \sum^\infty_{n_1= 1}\cdots \sum^\infty_{n_r=1} \chi_1(n_1)\cdots \chi_r(n_r)\cdot P(n+1+ a_1,\dots, n_r+ a_r)^{- s}, \] where \(a_i\geq 0\) and \(\chi_i\) is a Dirichlet character for each \(i\), and \(P\) is a polynomial satisfying certain conditions. First the analytic continuation of \(Z(P,\
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General congruences for Bernoulli polynomials
Discrete Mathematics, 2003 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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General convolution identities for Bernoulli and Euler polynomials
Journal of Mathematical Analysis and Applications, 2016 Using general identities for difference operators, as well as a technique of symbolic computation and tools from probability theory, we derive very general kth order (k \ge 2) convolution identities for Bernoulli and Euler polynomials. This is achieved by use of an elementary result on uniformly distributed random variables.
Ditcher, Karl, Vignat, Christophe
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