Results 11 to 20 of about 47,919 (237)

On the q-Extension of Apostol-Euler Numbers and Polynomials [PDF]

Abstract and Applied Analysis, 2008
Recently, Choi et al. (2008) have studied the -extensions of the Apostol-Bernoulli and the Apostol-Euler polynomials of order and multiple Hurwitz zeta function. In this paper, we define Apostol's type -Euler numbers and -Euler polynomials .
Young-Hee Kim, Wonjoo Kim, L. Jang
semanticscholar   +5 more sources

Note on q-extensions of Euler numbers and polynomials of higher order [PDF]

, 2007
In [14] Ozden-Simsek-Cangul constructed generating functions of higher-order twisted $(h,q)$-extension of Euler polynomials and numbers, by using $p$-adic q-deformed fermionic integral on $\Bbb Z_p$.
Jang, Leechae, Kim, Taekyun, Ryoo, Cheon-Seoung   +2 more
core   +4 more sources

Some Symmetric Identities for Degenerate Carlitz-type (p, q)-Euler Numbers and Polynomials

Symmetry, 2019
In this paper we define the degenerate Carlitz-type ( p , q ) -Euler polynomials by generalizing the degenerate Euler numbers and polynomials, degenerate Carlitz-type q-Euler numbers and polynomials.
Kyung-Won Hwang, Cheon Seoung Ryoo
exaly   +2 more sources

Some New Identities of Genocchi Numbers and Polynomials involving Bernoulli and Euler polynomials [PDF]

International Journal of Mathematics and Mathematical Sciences, 2013
In this paper, we will deal with some new formulae for two product Genocchi polynomials together with both Euler polynomials and Bernoulli polynomials. We get some applications for Genocchi polynomials.
Acikgoz, Mehmet, Araci, Serkan, Şen, Erdoğan   +2 more
core   +5 more sources

A Note on Some Identities of Frobenius-Euler Numbers and Polynomials [PDF]

International Journal of Mathematics and Mathematical Sciences, 2012
The purpose of this paper is to give some identities on the Frobenius-Euler numbers and polynomials by using the fermionic 𝑝-adic 𝑞-integral equation on ℤ𝑝.
Jongsoung Choi, Dae San Kim, Taekyun Kim, Y. H. Kim   +3 more
semanticscholar   +4 more sources

Laguerre-Type Bernoulli and Euler Numbers and Related Fractional Polynomials

Mathematics
We extended the classical Bernoulli and Euler numbers and polynomials to introduce the Laguerre-type Bernoulli and Euler numbers and related fractional polynomials.
Paolo Emilio Ricci, Rekha Srivastava, Diego Caratelli   +2 more
doaj   +2 more sources

Extended Laguerre Polynomials Associated with Hermite, Bernoulli, and Euler Numbers and Polynomials [PDF]

Abstract and Applied Analysis, 2012
Let 𝐏𝑛={𝑝(𝑥)∈ℝ[𝑥]∣deg𝑝(𝑥)≤𝑛} be an inner product space with the inner product ∫⟨𝑝(𝑥),𝑞(𝑥)⟩=∞0𝑥𝛼𝑒−𝑥𝑝(𝑥)𝑞(𝑥)𝑑𝑥, where 𝑝(𝑥),𝑞(𝑥)∈𝐏𝑛 and 𝛼∈ℝ with 𝛼g−1. In this paper we study the properties of the extended Laguerre polynomials which are an orthogonal basis ...
Taekyun Kim, Dae San Kim
semanticscholar   +4 more sources

Some identities related to degenerate Bernoulli and degenerate Euler polynomials

Mathematical and Computer Modelling of Dynamical Systems
The aim of this paper is to study degenerate Bernoulli and degenerate Euler polynomials and numbers and their higher-order analogues. We express the degenerate Euler polynomials in terms of the degenerate Bernoulli polynomials and vice versa.
Taekyun Kim, Dae San Kim, JongKyum Kwon   +2 more
exaly   +3 more sources

On the Symmetric Properties of Higher-Order Twisted q-Euler Numbers and Polynomials

Advances in Difference Equations, 2010
In 2009, Kim et al. gave some identities of symmetry for the twisted Euler polynomials of higher-order, recently. In this paper, we extend our result to the higher-order twisted q-Euler numbers and polynomials.
Sun-Jung Lee, Seog-Hoon Rim, Jeong-Hee Jin, Eun-Jung Moon   +3 more
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 ...
Luo, Qiu-Ming, Qi, Feng
core   +2 more sources