Results 151 to 160 of about 670 (184)

Identities related to the Bernoulli and the Euler numbers and polynomials

AIP Conference Proceedings, 2020
The main motivation of this paper is to investigate some properties of the generating functions for the numbers Yn(λ) and the polynomials Yn(x; λ), which were recently introduced by Simsek [9] and so we give some identities and relations including the numbers Yn(λ) and the polynomials Yn(x; λ), the Bernoulli numbers and polynomials, the Apostol ...
Busra Al, Mustafa Alkan
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Reciprocal relations of Bernoulli and Euler numbers/polynomials

Integral Transforms and Special Functions, 2018
ABSTRACTBy means of the symmetric summation theorem on polynomial differences due to Chu and Magli [Summation formulae on reciprocal sequences. European J Combin. 2007;28(3):921–930], we examine Bernoulli and Euler polynomials of higher order. Several reciprocal relations on Bernoulli and Euler numbers and polynomials are established, including some ...
Xiaoyuan Wang, Wenchang Chu
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Identities on the bernoulli and the euler numbers and polynomials

Ars Comb., 2012
International ...
Taekyun Kim 0001, Dae San Kim, Abdelmejid Bayad, Seog-Hoon Rim   +3 more
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Extended Zeilberger's algorithm for identities on Bernoulli and Euler polynomials [PDF]

Journal of Number Theory, 2009
We present a computer algebra approach to proving identities on Bernoulli polynomials and Euler polynomials by using the extended Zeilberger's algorithm given by Chen, Hou and Mu.
Lisa H Sun, William Y C Chen
exaly   +2 more sources

Identities for the Bernoulli and Euler numbers and polynomials.

Ars Comb., 2012
Summary: In this paper, we investigate some interesting identities on the Euler numbers and polynomials arising from their generating functions and difference operators. Finally, we give some properties of Bernoulli and Euler polynomials by using \(p\)-adic integral on \(\mathbb Z_p\).
Taekyun Kim 0001, B. Lee, S. H. Lee, Seog-Hoon Rim   +3 more
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Explicit formulas for the Bernoulli and Euler polynomials and numbers

Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, 1991
In this paper the main result (Theorem 2) gives the following formula for the Bernoulli polynomials \(B_ n(x)\) \[ (te^{tx}/(e^ t-1)=\sum^ \infty_{n=0}B_ n(x)t^ n/n!,\quad | t|
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Central Factorial Numbers and Values of Bernoulli and Euler Polynomials at Rationals

Numerical Functional Analysis and Optimization, 2009
The nth order derivatives of tan x and sec x may be represented by polynomials P n (u) and Q n (u) in u = tan x, which are known as the derivative polynomials for the tangent and secant and have occurred in diverse contexts. In this paper, explicit representations of P n (u) and Q n (u) are derived in terms of the central factorial numbers of the ...
Ching-Hua Chang, Chung-Wei Ha
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CLOSE LINKS OF BERNOULLI AND EULER NUMBERS AND POLYNOMIALS WITH SYMMETRIC FUNCTIONS

Rocky Mountain Journal of Mathematics
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bouzeraib, Meryem, Boussayoud, Ali, Saba, Nabiha, Aloui, Baghdadi   +3 more
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Some explicit formulas for the Bernoulli and Euler numbers and polynomials

International Journal of Mathematical Education in Science and Technology, 1988
A systematic investigation of various explicit representations for the Bernoulli and Euler numbers and polynomials is presented, and some interesting generalizations of these results are proved.
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Carlitz’s q-Bernoulli and q-Euler numbers and polynomials and a class of generalized q-Hurwitz zeta functions

Applied Mathematics and Computation, 2009
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Junesang Choi, P. J. Anderson, H. M. Srivastava 0001   +2 more
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