Results 41 to 50 of about 146,038 (187)
The Triangle Algorithm for Bernoulli Polynomials
, 2023 Algorithms like ones used to generate Pascal's triangle for generating Bernoulli polynomials and their various generalizations are given. It is remarkable that the algorithms for Bernoulli polynomials are natural interpolations of the ones for Bernoulli numbers.
Kawasaki, Naho, Ohno, Yasuo
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A Note on the Poly-Bernoulli Polynomials of the Second Kind
Journal of Function Spaces, 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.
Sang Jo Yun, Jin-Woo Park
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Asymptotic estimates for Apostol-Bernoulli and Apostol-Euler polynomials [PDF]
, 2012 We analyze the asymptotic behavior of the Apostol-Bernoulli polynomials Bn(x; λ) 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. [0000-0002-5742-8679] +5 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.
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Some Determinantal Expressions and Recurrence Relations of the Bernoulli Polynomials
Mathematics, 2016 In the paper, the authors recall some known determinantal expressions in terms of the Hessenberg determinants for the Bernoulli numbers and polynomials, find alternative determinantal expressions in terms of the Hessenberg determinants for the Bernoulli ...
Feng Qi, Bai-Ni Guo
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A Note on the (ℎ,𝑞)-Extension of Bernoulli Numbers and Bernoulli Polynomials
Discrete Dynamics in Nature and Society, 2010 We observe the behavior of roots of the (ℎ,𝑞)-extension of Bernoulli polynomials 𝐵(ℎ)𝑛,𝑞(𝑥). By means of numerical experiments, we demonstrate a remarkably regular structure of the complex roots of the q-extension of Bernoulli polynomials 𝐵(ℎ)𝑛,𝑞(𝑥). The
C. S. Ryoo, T. Kim
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Degenerate poly-type 2-bernoulli polynomials [PDF]
, 2021 Recently, Kim-Kim [10] have studied type 2-Changhee and Daehee polynomials. They have also introduced the type 2-Bernoulli polynomials in order to express the central factorial numbers of the second kind by making use of type 2-Bernoulli numbers of ...
Serkan ARACI
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On generalized Bernoulli-Barnes polynomials [PDF]
, 2022 The main purpose of this paper is to introduce some generalizations of the Bernoulli-Barnes polynomials. These generalizations come from suitable modifications of the Mittag-Leffler type function linked to the generating function corresponding to the ...
Sirvent, Víctor F. +2 more
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Congruences for Bernoulli numbers and Bernoulli polynomials
Discrete Mathematics, 1997 The Bernoulli numbers and polynomials are defined by \(B_0=1\), \(\sum^{n-1}_{k=0}{n\choose k} B_k= 0\) \((n=2,3,\dots)\) and \(B_n(x)= \sum^n_{k=0}{n\choose k} B_{n-k} x^k\), respectively. Two basic congruences for Bernoulli numbers are the Kummer congruences (used in the theory of Fermat's last theorem) and the von Staudt-Clausen theorem. There exist
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On the Symmetries of the q‐Bernoulli Polynomials [PDF]
Abstract and Applied Analysis, 2008 Kupershmidt and Tuenter have introduced reflection symmetries for the q‐Bernoulli numbers and the Bernoulli polynomials in (2005), (2001), respectively. However, they have not dealt with congruence properties for these numbers entirely. Kupershmidt gave a quantization of the reflection symmetry for the classical Bernoulli polynomials. Tuenter derived a
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