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Euler and the Strong Law of Small Numbers [PDF]
The American Mathematical Monthly, 2016 We identify and correct an erroneous formula for Euler numbers that appears in Hansen's Table of Series and Products. We also provide details about the history of this error.
Dilcher, Karl, Vignat, Christophe
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Some identities on degenerate poly-Euler polynomials arising from degenerate polylogarithm functions
Applied Mathematics in Science and Engineering, 2023 Our main focus here is a new type of degenerate poly-Euler polynomials and numbers. This focus stems from their nascent importance for applications in combinatorics, number theory and in other aspects of applied mathematics.
Lingling Luo +3 more
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Generalized -Euler Numbers and Polynomials [PDF]
ISRN Applied Mathematics, 2012 We generalize the Euler numbers and polynomials by the generalized -Euler numbers and polynomials . For the complement theorem, have interesting different properties from the Euler polynomials and we observe an interesting phenomenon of “scattering” of the zeros of the the generalized Euler polynomials in complex plane.
Lee, Hui Young +2 more
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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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On generalized Lucas polynomials and Euler numbers [PDF]
, 2010 In this paper we study the relationship between the generalized Lucas polynomials and the Euler numbers and give several interesting identities involving ...
Nalli, Ayse +2 more
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A Note on the q-Euler Measures
Advances in Difference Equations, 2009 Properties of q-extensions of Euler numbers and polynomials which generalize those satisfied by Ek and Ek(x) are used to construct q-extensions of p-adic Euler measures and define p-adic q-ℓ-series which interpolate q-Euler numbers at negative ...
Taekyun Kim +2 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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ON TWISTED GENERALIZED EULER NUMBERS [PDF]
Bulletin of the Korean Mathematical Society, 2004 Summary: In this paper, we construct generating function of twisted generalized Euler numbers \[ \frac{1-u}{e^t-u}\sum^\infty_{n=0}H^n(u)\frac{t^n}{n!}. \] By using this function, we define twisted generalized Euler polynomials and numbers. We give some basic properties of these polynomials and numbers.
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A Note on Euler Numbers and Polynomials [PDF]
Nagoya Mathematical Journal, 1954 Let Em denote the Euler number in the even suffix notation so that(1.1) where, as usual, after expansion of the left member Er is replaced by Er. Nielsen [4, p. 273] has proved that(1.2)
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Some identities and congruences concerning Euler numbers and polynomials
, 2010 In this paper, using the properties of the moments of p-adic measures, we establish some identities and Kummer likewise congruences concerning Euler numbers and polynomials.
Hamadoun Maïga, Maïga, Hamadoun
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