Results 31 to 40 of about 1,076 (103)
Mathematics, 2022 Numerous polynomial variations and their extensions have been explored extensively and found applications in a variety of research fields. The purpose of this research is to establish a unified class of Apostol–Genocchi polynomials based on poly-Daehee ...
Talha Usman +5 more
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Asymptotic estimates for Apostol-Bernoulli and Apostol-Euler polynomials [PDF]
Mathematics of Computation, 2012 We analyze the asymptotic behavior of the Apostol-Bernoulli polynomials $\mathcal{B}_{n}(x; )$ in detail. The starting point is their Fourier series on $[0,1]$ which, it is shown, remains valid as an asymptotic expansion over compact subsets of the complex plane.
Navas, L.M., Ruiz, F.J., Varona, J.L.
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A Note on the Poly‐Bernoulli Polynomials of the Second Kind
Journal of Function Spaces, Volume 2020, Issue 1, 2020., 2020 In this paper, we define the poly‐Bernoulli polynomials of the second kind by using the polyexponential function and find some interesting identities of those polynomials. In addition, we define unipoly‐Bernoulli polynomials of the second kind and study some properties of those polynomials.
Sang Jo Yun, Jin-Woo Park, Serkan Araci
wiley +1 more source
Mathematics, 2023 The purpose of this article is to give relations among the uniform B-splines, the Bernstein basis functions, and certain families of special numbers and polynomials with the aid of the generating functions method.
Yilmaz Simsek
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A Unified Family of Generalized $q$-Hermite Apostol Type Polynomials and its Applications
Communications in Advanced Mathematical Sciences, 2019 The intended objective of this paper is to introduce a new class of generalized $q$-Hermite based Apostol type polynomials by combining the $q$-Hermite polynomials and a unified family of $q$-Apostol-type polynomials.
Tabinda Nahid, Subuhi Khan
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Several identities for the generalized Apostol–Bernoulli polynomials
Computers & Mathematics with Applications, 2008 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhang, Zhizheng, Yang, Hanqing
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Sums of products of Apostol-Bernoulli and Apostol-Euler polynomials [PDF]
Advances in Difference Equations, 2014 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Araci, Serkan, He, Yuan
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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 a class of $q$-Bernoulli, $q$-Euler and $q$-Genocchi polynomials [PDF]
, 2014 The main purpose of this paper is to introduce and investigate a class of $q$-Bernoulli, $q$-Euler and $q$-Genocchi polynomials. The $q$-analogues of well-known formulas are derived.
Mahmudov, N. I., Momenzadeh, M.
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Möbius inversion formulae for Apostol-Bernoulli type polynomials and numbers [PDF]
Mathematics of Computation, 2013 Summary: In this paper, we establish Möbius inversion formulae for the Fourier expansions of the Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials. As an application, by specializing our formulae at some special values we obtain interesting number-theoritical relations. We derive explicit formulae for Apostol-Bernoulli numbers.
Bayad, Abdelmejid, Chikhi, J.
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