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Relationships between generalized Bernoulli numbers and polynomials and generalized Euler numbers and polynomials. [PDF]

open access: yes, 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
core   +8 more sources

A New Type of Euler Polynomials and Numbers

Mediterranean Journal of Mathematics, 2018
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Masjed-Jamei, M.   +2 more
openaire   +2 more sources

A Simple Generalization of Euler Numbers and Polynomials

Journal of the Indian Mathematical Society, 2018
In this article, we shall consider a generalization of Euler's numbers and polynomials based on modifying the corresponding generating function. We shall prove some recurrence relations, an explicit formula, and multiplicative properties of the generalized numbers.
Hassen, Abdul, Ernst, Christopher R.
openaire   +2 more sources

A note on generalized Euler numbers and polynomials

International Journal of Computer Mathematics, 2007
In this paper we construct new generalized Euler polynomials and generalized Euler numbers attached to χ. We investigate some of the properties that are related to generalized Euler polynomials. We also derive the existence of a specific interpolation function that interpolates generalized Euler polynomials at negative integers. Finally, we investigate
Cheon Seoung Ryoo   +2 more
openaire   +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   +3 more
openaire   +2 more sources

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