Results 101 to 110 of about 18,359 (203)
Evaluation of cauchy polynomials via degenerate r-Stirling numbers
Mathematical and Computer Modelling of Dynamical SystemsIn this paper, within the framework of unsigned degenerate [Formula: see text]-Stirling numbers, we establish connections among Cauchy polynomials, degenerate Bernoulli polynomials, and degenerate hyperharmonic numbers.
Zhuoyu Chen +4 more
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Algebraic Structures of Bernoulli Numbers and Polynomials
, 2012 In a field of Laurent series, we construct a subring which has a module structure over a Weyl algebra. Identities of Bernoulli numbers and polynomials are obtained from these algebraic structures.Comment: This article was submitted to J. Number Theory on
Huang, I-Chiau
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Arithmetic Properties of Bernoulli–Padé Numbers and Polynomials
Journal of Number Theory, 2002 Let \(r,s\) be nonnegative integers. The authors define rational numbers \(B_n^{(r,s)}\), the \(n\)th Bernoulli-Padé numbers of order \((r,s)\), by the formula \[ \frac{(-1)^sr!s!t^{r+s+1}}{(r+s)!(r+s+1)!(Q^{(r,s)}(t)e^t- P^{(r,s)}(t))} = \sum_{n=0}^\infty B_n^{(r,s)}\frac{t^n}{n!}, \] where \(P^{(r,s)}(t)\) and \(Q^{(r,s)}(t)\) are polynomials (given ...
Dilcher, Karl, Louise, Louise
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A new construction on the
Advances in Difference Equations, 2011 This paper performs a further investigation on the q-Bernoulli polynomials and numbers given by Açikgöz et al. (Adv. Differ. Equ. 2010, 9, Article ID 951764) some incorrect properties are revised.
Bayad Abdelmejid +4 more
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Behavioral Modeling of Memristors under Harmonic Excitation. [PDF]
Micromachines (Basel), 2023 Solovyeva E, Serdyuk A.
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ON RECURRENCE RELATIONS FOR BERNOULLI POLYNOMIALS AND NUMBERS
Facta Universitatis, Series: Mathematics and InformaticsIn this work we connect Bernoulli numbers and polynomials to Mersenne numbers via recurrence relations. We find two explicit formulas of Bernoulli numbers by means of Mersenne numbers different from those given by F. Qi and X. Y. Chen et al. To end with other interesting relationships, which serve as bridges between the Bernoulli polynomials and ...
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Generalizations of the Bernoulli and Appell polynomials
Abstract and Applied Analysis, 2004 We first introduce a generalization of the Bernoulli polynomials, and consequently of the Bernoulli numbers, starting from suitable generating functions related to a class of Mittag-Leffler functions.
Gabriella Bretti +2 more
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Anharmonic polynomial generalizations of the numbers of Bernoulli and Euler [PDF]
Transactions of the American Mathematical Society, 1922 We consider twelve infinite systems of polynomials in z which for z = 1 degenerate either to the numbers of Bernoulli or Euler, or to others simply dependent upon these. The first part proceeds from the definition of anharmonic polynomials to the specific twelve systems discussed; the second presents an adaptation of the symbolic calculus of Blissard ...
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Probabilistic degenerate Bernoulli and degenerate Euler polynomials
Mathematical and Computer Modelling of Dynamical SystemsRecently, many authors have studied degenerate Bernoulli and degenerate Euler polynomials. Let [Formula: see text] be a random variable whose moment generating function exists in a neighbourhood of the origin.
Lingling Luo +3 more
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Journal of Applied Mathematics, 2013 Recently, many mathematicians have studied different kinds of the Euler, Bernoulli, and Genocchi numbers and polynomials. In this paper, we give another definition of polynomials Ũn(x).
J. Y. Kang, C. S. Ryoo
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