Results 141 to 150 of about 209 (173)

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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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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CLOSE LINKS OF BERNOULLI AND EULER NUMBERS AND POLYNOMIALS WITH SYMMETRIC FUNCTIONS

Rocky Mountain Journal of Mathematics
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Bouzeraib, Meryem, Boussayoud, Ali, Saba, Nabiha, Aloui, Baghdadi   +3 more
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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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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
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Junesang Choi, P. J. Anderson, H. M. Srivastava 0001   +2 more
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Summation formulae for Genocchi, Bernoulli, and Euler numbers and polynomials

Proceedings of the Romanian Academy, Series A: Mathematics, Physics, Technical Sciences, Information Science
By means of two known combinatorial identities involving polynomials, recurrence relations, and the telescoping technique, we obtain new explicit expressions for Genocchi, Bernoulli and Euler numbers/polynomials, along with some other interesting transformation formulas and explicit double sum combinatorial identities.
Dongwei GUO, Yingming ZHU, Yulei CHEN
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Relationships between generalized Bernoulli numbers and polynomials and generalized Euler numbers and polynomials.

2002
Let \(a,b,c\) be positive numbers. The generalized Bernoulli and Euler numbers are defined via the generating functions \(\frac{t}{b^t-a^t}\) and \(\frac{2c^t}{b^{2t}+a^{2t}}\) respectively, so that the classical sequences are obtained if \(a=1\), \(b=c=e\). A generalization of the Bernoulli and Euler polynomials is introduced in a similar way.
Luo, Qiu-Ming, Qi, Feng
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Basic Bernoulli and Euler Polynomials and Numbers and q-Zeta Function

2003
Certain q-Fourier expansions found in the previous chapter give us a possibility to introduce analogs of the Bernoulli polynomials and numbers, the Euler polynomials and numbers, and the Riemann zeta function [146]. We shall study some of their properties that are close to the classical ones.
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