Results 21 to 30 of about 209 (173)
Anharmonic polynomial generalizations of the numbers of Bernoulli and Euler [PDF]
Transactions of the American Mathematical Society, 1922 We consider twelve infinite systems of polynomials in z which for z = 1 degenerate either to the numbers of Bernoulli or Euler, or to others simply dependent upon these. The first part proceeds from the definition of anharmonic polynomials to the specific twelve systems discussed; the second presents an adaptation of the symbolic calculus of Blissard ...
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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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Some results for the q-Bernoulli, q-Euler numbers and polynomials [PDF]
Advances in Difference Equations, 2011 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kim, D Kim, Daeyeoul +1 more
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Symmetry, 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, the sine-Bernoulli polynomials, the cosine-Euler polynomials, and the sine-Euler polynomials.
Bayad, Abdelmejid, Simsek, Yilmaz
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Generalized Tepper’s Identity and Its Application
Mathematics, 2020 The aim of this paper is to study the Tepper identity, which is very important in number theory and combinatorial analysis. Using generating functions and compositions of generating functions, we derive many identities and relations associated with the ...
Dmitry Kruchinin +2 more
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Some identities related to degenerate Stirling numbers of the second kind
Demonstratio Mathematica, 2022 The degenerate Stirling numbers of the second kind were introduced as a degenerate version of the ordinary Stirling numbers of the second kind. They appear very frequently when one studies various degenerate versions of some special numbers and ...
Kim Taekyun, Kim Dae San, Kim Hye Kyung
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Explicit Formulas Involving -Euler Numbers and Polynomials
Abstract and Applied Analysis, 2012 We deal with -Euler numbers and -Bernoulli numbers. We derive some interesting relations for -Euler numbers and polynomials by using their generating function and derivative operator.
Serkan Araci +2 more
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Combinatorial aspects of poly-Bernoulli polynomials and poly-Euler numbers
Journal de théorie des nombres de Bordeaux, 2023 In this article, we introduce combinatorial models for poly-Bernoulli polynomials and poly-Euler numbers of both kinds. As their applications, we provide combinatorial proofs of some identities involving poly-Bernoulli polynomials.
Bényi, Beáta, Matsusaka, Toshiki
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Duals of Bernoulli Numbers and Polynomials and Euler Number and Polynomials
, 2015 A sequence inverse relationship can be defined by a pair of infinite inverse matrices. If the pair of matrices are the same, they define a dual relationship. Here presented is a unified approach to construct dual relationships via pseudo-involution of Riordan arrays.
He, Tian-Xiao, Zheng, Jinze
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Journal of Applied Mathematics, 2013 Recently, many mathematicians have studied different kinds of the Euler, Bernoulli, and Genocchi numbers and polynomials. In this paper, we give another definition of polynomials Ũn(x).
J. Y. Kang, C. S. Ryoo
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