Fourier expansions for higher-order Apostol–Genocchi, Apostol–Bernoulli and Apostol–Euler polynomials [PDF]
Advances in Difference Equations, 2020 Fourier expansions of higher-order Apostol–Genocchi and Apostol–Bernoulli polynomials are obtained using Laurent series and residues. The Fourier expansion of higher-order Apostol–Euler polynomials is obtained as a consequence.
Cristina B. Corcino, Roberto B. Corcino
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Some Formulae of Products of the Apostol-Bernoulli and Apostol-Euler Polynomials [PDF]
Discrete Dynamics in Nature and Society, 2012 Some formulae of products of the Apostol-Bernoulli and Apostol-Euler polynomials are established by applying the generating function methods and some summation transform techniques, and various known results are derived as special cases.
Yuan He, Chunping Wang
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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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Identities and recurrence relations of special numbers and polynomials of higher order by analysis of their generating functions. [PDF]
J Inequal Appl, 2018 The aim of this is to give generating functions for new families of special numbers and polynomials of higher order. By using these generating functions and their functional equations, we derive identities and relations for these numbers and polynomials.
Simsek Y, Kim D.
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Higher-Order Convolutions for Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi Polynomials [PDF]
Mathematics, 2018 In this paper, we present a systematic and unified investigation for the Apostol-Bernoulli polynomials, the Apostol-Euler polynomials and the Apostol-Genocchi polynomials. By applying the generating-function methods and summation-transform techniques, we
Yuan He +3 more
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On the apostol-bernoulli polynomials
Open Mathematics, 2004 Abstract In the present paper, we obtain two new formulas of the Apostol-Bernoulli polynomials (see On the Lerch Zeta function. Pacific J. Math., 1 (1951), 161–167.), using the Gaussian hypergeometric functions and Hurwitz Zeta functions respectively, and give certain special cases and applications.
Luo Qiu-Ming
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Parametric kinds of generalized Apostol-Bernoulli polynomials and their properties
, 2023 The purpose of this paper is to define generalized Apostol--Bernoulli polynomials with including a new cosine and sine parametric type of generating function using the quasi-monomiality properties and trigonometric functions.
Kızılateş, Can +3 more
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Karpatsʹkì Matematičnì Publìkacìï, 2022 The aim of this paper is to study new classes of degenerated generalized Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials of order $\alpha$ and level $m$ in the variable $x$. Here the degenerate polynomials are a natural extension of the
W. Ramírez, C. Cesarano
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Two Nice Determinantal Expressions and a Recurrence Relation for the Apostol--Bernoulli Polynomials [PDF]
Journal of the Indonesian Mathematical Society, 2017 In the paper, the authors establish two nice determinantal expressions and a recurrence relation for the Apostol--Bernoulli ...
Guo, B. (Bai-Ni), Qi, F. (Feng)
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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.
Burak Kurt
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