Results 61 to 70 of about 726,471 (254)
, 2020 A numerical inverse Laplace transform method is established using Bernoulli polynomials operational matrix of integration. The efficiency of the method is demonstrated through some standard nonlinear differential equations: Duffing equation, Van der Pol ...
D. Rani, Vinod Mishra
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A degenerate version of hypergeometric Bernoulli polynomials: announcement of results
Communications in Applied and Industrial MathematicsThis article explores some properties of degenerate hypergeometric Bernoulli polynomials, which are defined through the following generating function tmeλx(t)eλx(t)-∑l=0m-1(1)l,λtll!=∑n=0∞Bn,λ[m-1](x)tnn!, |t|
Yamilet Quintana, William Ramírez
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A Study of Szász–Durremeyer-Type Operators Involving Adjoint Bernoulli Polynomials
MathematicsThis research work introduces a connection of adjoint Bernoulli’s polynomials and a gamma function as a sequence of linear positive operators. Further, the convergence properties of these sequences of operators are investigated in various functional ...
Nadeem Rao, M. Farid, Rehan Ali
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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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Parametric kinds of generalized Apostol-Bernoulli polynomials and their properties [PDF]
, 2023 The purpose of this paper is to define generalized Apostol--Bernoulli polynomials with including a new cosine and sine parametric type of generating function using the quasi-monomiality properties and trigonometric functions.
Qi, Feng +3 more
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Rota-Baxter operators and Bernoulli polynomials
, 2021 summary:We develop the connection between Rota-Baxter operators arisen from algebra and mathematical physics and Bernoulli polynomials. We state that a trivial property of Rota-Baxter operators implies the symmetry of the power sum polynomials and ...
Gubarev, Vsevolod, Vsevolod Gubarev
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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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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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Mathematical methods in the applied sciencesAlthough it is very easy to calculate the 1st moment and 2nd moment values of the geometric distribution with the methods available in existing books and other articles, it is quite difficult to calculate moment values larger than the 3rd order.
Buket Şimşek
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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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