Results 31 to 40 of about 26,237 (204)
A Parametric Type of Cauchy Polynomials with Higher Level
Axioms, 2021 There are many kinds of generalizations of Cauchy numbers and polynomials. Recently, a parametric type of the Bernoulli numbers with level 3 was introduced and studied as a kind of generalization of Bernoulli polynomials.
Takao Komatsu
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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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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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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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Old and New Identities for Bernoulli Polynomials via Fourier Series
International Journal of Mathematics and Mathematical Sciences, 2012 The Bernoulli polynomials Bk restricted to [0,1) and extended by periodicity have nth sine and cosine Fourier coefficients of the form Ck/nk. In general, the Fourier coefficients of any polynomial restricted to [0,1) are linear combinations of terms of ...
Luis M. Navas +2 more
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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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Mathematics, 2020 In this paper, we define cosine Bernoulli polynomials and sine Bernoulli polynomials related to the q-number. Furthermore, we intend to find the properties of these polynomials and check the structure of the roots.
Jung Yoog Kang, Chen Seoung Ryoo
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New Characterization of Appell polynomials
, 2016 We prove characterizations of Appell polynomials by means of symmetric property. For these polynomials, we establish a simple linear expression in terms of Bernoulli and Euler polynomials. As applications, we give interesting examples.
Bayad, Abdelmejid, Komatsu, Takao
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Bernoulli Related Polynomials and Numbers [PDF]
Mathematics of Computation, 1979 The polynomials φ n ( x ; a , b ) {\varphi _n}(x;a,b) of degree n defined by the equations \[ Δ a φ n ( x
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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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