On Generating Functions for Parametrically Generalized Polynomials Involving Combinatorial, Bernoulli and Euler Polynomials and Numbers [PDF]
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.
Abdelmejid Bayad, Yılmaz Şimşek
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Closed formulas and determinantal expressions for higher-order Bernoulli and Euler polynomials in terms of Stirling numbers [PDF]
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2021 In this paper, applying the Fa di Bruno formula and some properties of Bell polynomials, several closed formulas and determinantal expressions involving Stirling numbers of the second kind for higher-order Bernoulli and Euler polynomials are presented.
Muhammet Cihat Dağlı
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Explicit relations on the degenerate type 2-unified Apostol–Bernoulli, Euler and Genocchi polynomials and numbers [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 The main aim of this paper is to introduce and investigate the degenerate type 2-unified Apostol–Bernoulli, Euler and Genocchi polynomials by using monomiality principle and operational methods. We give explicit relations and some identities for the degenerate type 2-unified Apostol–Bernoulli, Euler and Genocchi polynomials.
Burak Kurt
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Duals of Bernoulli Numbers and Polynomials and Euler Number and Polynomials [PDF]
, 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.
Tian-Xiao He, Jinze Zheng
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Combinatorial aspects of poly-Bernoulli polynomials and poly-Euler numbers [PDF]
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.
Beáta Bényi, Toshiki Matsusaka
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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.
Daeyeoul Kim, Min-Soo Kim
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Identities associated with Milne–Thomson type polynomials and special numbers [PDF]
Journal of Inequalities and Applications, 2018 The purpose of this paper is to give identities and relations including the Milne–Thomson polynomials, the Hermite polynomials, the Bernoulli numbers, the Euler numbers, the Stirling numbers, the central factorial numbers, and the Cauchy numbers.
Yilmaz Simsek, Nenad Cakic
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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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A parametric unified Apostol-type Bernoulli, Euler, Genocchi, Fubini polynomials and numbers
Filomat, 2023 In recent years, mathemacians ([1], [3], [5], [22], [23]) introduced and investigated the Fubini Apostol-type numbers and polynomials. They gave some recurrence relations explicit properties and identities for these polynomials. In [12], author considered unified degenerate Apostol-type Bernoulli, Euler, Genocchi and Fubini polynomials and ...
Burak Kurt
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Some Identities for the Bernoulli, the Euler and the Genocchi Numbers and Polynomials [PDF]
, 2009 The purpose of this paper is to give some new identities for the Bernoulli, the Euler and the Genocchi numbers and polynomials.
Taekyun Kim
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