Results 41 to 50 of about 1,776 (233)
Axioms, 2022 In this paper, the Fourier series expansion of Tangent polynomials of higher order is derived using the Cauchy residue theorem. Moreover, some variations of higher-order Tangent polynomials are defined by mixing the concept of Tangent polynomials with ...
Cristina Bordaje Corcino +1 more
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Generalised Bernoulli polynomials and series [PDF]
Bulletin of the Australian Mathematical Society, 2000 We present several results related to the recently introduced generalised Bernoulli polynomials. Some recurrence relations are given, which permit us to compute efficiently the polynomials in question. The sums , where jk = jk (α) are the zeros of the Bessel function of the first kind of order α, are evaluated in terms of these polynomials.
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Degenerate poly-type 2-bernoulli polynomials
, 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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Some Identities on the q-Bernoulli Numbers and Polynomials with Weight 0
Abstract and Applied Analysis, 2011 Recently, Kim (2011) has introduced the q-Bernoulli numbers with weight α. In this paper, we consider the q-Bernoulli numbers and polynomials with weight α=0 and give p-adic q-integral representation of Bernstein polynomials associated ...
T. Kim, J. Choi, Y. H. Kim
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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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Bernoulli Related Polynomials and Numbers [PDF]
Mathematics of Computation, 1979 The polynomials φ
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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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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 identities related to degenerate Bernoulli and degenerate Euler polynomials
Mathematical and Computer Modelling of Dynamical SystemsThe aim of this paper is to study degenerate Bernoulli and degenerate Euler polynomials and numbers and their higher-order analogues. We express the degenerate Euler polynomials in terms of the degenerate Bernoulli polynomials and vice versa.
Taekyun Kim +3 more
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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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