Results 251 to 260 of about 852,038 (290)

Bernoulli and Euler Polynomials

2021
Focus of this chapter are Bernoulli numbers and polynomials, and Euler numbers and polynomials in the complex domain. For the evaluation several methods can be used in dependence of the polynomial degree and argument: Direct integration, direct integration in combination with argument transformations, or expansions with respect to trigonometric series.
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Generalized Euler-Frobenius Polynomials

Zeitschrift für Analysis und ihre Anwendungen, 1995
The solution of the two-dimensional difference equation \(a_{n + 1, \nu + 1} = a_{n + 1, \nu} + (1 - z) a_{n \nu}\) is obtained. Applications are presented.
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The Euler–Frobenius Polynomials

2014
The Euler–Frobenius polynomials have been throughout the book to characterize asymptotic sampling zeros in discrete models as the sampling period goes to zero. This chapter presents a brief historical account of these polynomials, and a summary of (equivalent) definitions and properties found in the literature.
Juan I. Yuz, Graham C. Goodwin
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Bernoulli and Euler Polynomials in Clifford Analysis

Advances in Applied Clifford Algebras, 2014
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hassan, G. F., Aloui, L.
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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.
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ON THE GENERALIZED EULER POLYNOMIALS OF THE SECOND KIND

Journal of applied mathematics & informatics, 2013
The authors define generalized Euler numbers and polynomials of the second kind as follows: \[ \left(\frac{2e^t}{e^{2t}+1}\right)^x=\sum_{n=0}^\infty \tilde{\mathcal E_n}(x)\frac{t^n}{n!}\qquad (| t|
Kim, Y. H., Jung, H. Y., Ryoo, C. S.
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Euler's Theorem for Polynomials

Mathematics Magazine, 1992
(1992). Euler's Theorem for Polynomials. Mathematics Magazine: Vol. 65, No. 5, pp. 334-335.
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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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Solving fractional-order delay integro-differential equations using operational matrix based on fractional-order Euler polynomials

, 2020
S. Rezabeyk, S. Abbasbandy, E. Shivanian
semanticscholar   +1 more source

Moment Representations of Fully Degenerate Bernoulli and Degenerate Euler Polynomials

Russian journal of mathematical physics
D. Kim, T. Kim
semanticscholar   +1 more source