Results 31 to 40 of about 1,656 (235)
A note on Euler number and polynomials [PDF]
Journal of Inequalities and Applications, 2006 The multiple Euler polynomials of \(p\)-adic arguments are defined via a \(p\)-adic integration procedure proposed by \textit{T. Kim} [J. Number Theory 76, No. 2, 320--329 (1999; Zbl 0941.11048)]. The authors give a formula for a sum of products of Euler polynomials. This answers a question by \textit{I.-C. Huang} and \textit{S.-Y. Huang} [J.
Kim Seoung-Dong +3 more
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Stirling Numbers and Spin-Euler Polynomials [PDF]
Experimental Mathematics, 2007 The Fischer decomposition on ℝn gives the decomposition of arbitrary homogeneous polynomials in n variables (x 1, . . . , x n) in terms of harmonic homogeneous polynomials. In classical Clifford analysis a refinement was obtained, giving a decomposition in terms of monogenic polynomials, i.e., homogeneous null solutions for the Dirac operator (a vector-
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A NOTE ON THE q-ANALOGUES OF EULER NUMBERS AND POLYNOMIALS [PDF]
Honam Mathematical Journal, 2011 Summary: In this paper, we consider the \(q\)-analogues of Euler numbers and polynomials using the fermionic \(p\)-adic invariant integral on \(\mathbb Z_p\). From these numbers and polynomials, we derive some interesting identities and properties on the \(q\)-analogues of Euler numbers and polynomials.
Choi, Jongsung +2 more
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Mathematics, 2021 In this paper, we further study the generating function involving a variety of special numbers and ploynomials constructed by the second author. Applying the Mellin transformation to this generating function, we define a new class of zeta type functions,
Daeyeoul Kim, Yilmaz Simsek
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, 2022 The aim of this paper is to give generating functions for parametrically generalized polynomials that are related to the combinatorial numbers, the Bernoulli polynomials and numbers, the Euler polynomials and numbers, the cosine-Bernoulli polynomials ...
Abdelmejid Bayad +3 more
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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 fermionicp-adicq-integral equation onℤp.
Jongsoung Choi +3 more
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Hermite Polynomials and their Applications Associated withBernoulli and Euler Numbers [PDF]
Discrete Dynamics in Nature and Society, 2012 We derive some interesting identities and arithmetic properties of Bernoulli and Euler polynomials from the orthogonality of Hermite polynomials. LetPn= {p(x) ∈ℚ[x]∣deg p(x) ≤n} be the (n+ 1)‐dimensional vector space overℚ. Then we show that {H0(x),H1(x), …,Hn(x)} is a good basis for the spacePnfor our purpose of arithmetical and combinatorial ...
Dae San Kim +3 more
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Special Numbers and Polynomials Including Their Generating Functions in Umbral Analysis Methods
Axioms, 2018 In this paper, by applying umbral calculus methods to generating functions for the combinatorial numbers and the Apostol type polynomials and numbers of order k, we derive some identities and relations including the combinatorial numbers, the Apostol ...
Yilmaz Simsek
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Multivariate Interpolation Functions of Higher-Order q-Euler Numbers and Their Applications
Abstract and Applied Analysis, 2008 The aim of this paper, firstly, is to construct generating functions of q-Euler numbers and polynomials of higher order by applying the fermionic p-adic q-Volkenborn integral, secondly, to define multivariate q-Euler zeta function (Barnes-type Hurwitz q ...
Hacer Ozden +2 more
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A Note on Type 2 Degenerate q-Euler Polynomials
Mathematics, 2019 Recently, type 2 degenerate Euler polynomials and type 2 q-Euler polynomials were studied, respectively, as degenerate versions of the type 2 Euler polynomials as well as a q-analog of the type 2 Euler polynomials.
Taekyun Kim +3 more
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