Results 11 to 20 of about 146,038 (187)
Bernoulli Basis and the Product of Several Bernoulli Polynomials [PDF]
International Journal of Mathematics and Mathematical Sciences, 2012 We develop methods for computing the product of several Bernoulli and Euler polynomials by using Bernoulli basis for the vector space of polynomials of degree less than or equal to n.
Dae San Kim, Taekyun Kim
doaj +4 more sources
Old and New Identities for Bernoulli Polynomials via Fourier Series [PDF]
International Journal of Mathematics and Mathematical Sciences, 2012 The Bernoulli polynomials Bk restricted to [0,1) and extended by periodicity have nth sine and cosine Fourier coefficients of the form Ck/nk. In general, the Fourier coefficients of any polynomial restricted to [0,1) are linear combinations of terms of ...
Luis M. Navas +2 more
doaj +2 more sources
A Note on Symmetric Properties of the Twisted q-Bernoulli Polynomials and the Twisted Generalized q-Bernoulli Polynomials [PDF]
Advances in Difference Equations, 2010 We define the twisted q-Bernoulli polynomials and the twisted generalized q-Bernoulli polynomials attached to χ of higher order and investigate some symmetric properties of them. Furthermore, using these symmetric properties of them, we can obtain
L.-C. Jang +5 more
doaj +2 more sources
Lagrange-Based Hypergeometric Bernoulli Polynomials [PDF]
Symmetry, 2022 Special polynomials play an important role in several subjects of mathematics, engineering, and theoretical physics. Many problems arising in mathematics, engineering, and mathematical physics are framed in terms of differential equations. In this paper,
Sahar Albosaily +7 more
core +4 more sources
p-Bernoulli and geometric polynomials
International Journal of Number Theory, 2018 We relate geometric polynomials and [Formula: see text]-Bernoulli polynomials with an integral representation, then obtain several properties of [Formula: see text]-Bernoulli polynomials.
Levent Kargın
core +2 more sources
Fully degenerate poly-Bernoulli numbers and polynomials
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
doaj +2 more sources
Relationships Between Generalized Bernoulli Numbers and Polynomials and Generalized Euler Numbers and Polynomials [PDF]
, 2002 In this paper, concepts of the generalized Bernoulli and Euler numbers and polynomials are introduced, and some relationships between them are ...
Qi, Feng, Luo, Qiu-Ming
core +6 more sources
Generalizations and Refinements of Hermite-Hadamard's Inequality [PDF]
, 2001 In this article, with the help of concept of the harmonic sequence of polynomials, the well known Hermite-Hadamard’s inequality for convex functions is generalied to the cases with bounded derivatives of n-th order, including the so-called n-convex ...
Qi, Feng, Yang, Qiao, Wei, Zong-Li
core +6 more sources
Values of Bernoulli polynomials [PDF]
Pacific Journal of Mathematics, 1996 The main objective of this paper is to derive a formula for the expression \(B_{p-1} (a/q)- B_{p- 1}\bmod p\). Here, \(p\) is an odd prime, \(q\) and \(a\) are relatively prime integers, \(1\leq a\leq q\), and \(p\) does not divide \(q\). \(B_n\) means the Bernoulli number and \(B_n (t)\) the \(n\)th Bernoulli polynomial.
Granville, Andrew, Sun, Zhi-Wei
openaire +3 more sources
Rota-Baxter operators and Bernoulli polynomials [PDF]
, 2021 summary:We develop the connection between Rota-Baxter operators arisen from algebra and mathematical physics and Bernoulli polynomials. We state that a trivial property of Rota-Baxter operators implies the symmetry of the power sum polynomials and ...
Gubarev, Vsevolod
core +1 more source