scholarly journals Some Identities of the Twisted 𝑞-Genocchi Numbers and Polynomials with Weight 𝛼 and 𝑞-Bernstein Polynomials with Weight 𝛼

2011 ◽  
Vol 2011 ◽  
pp. 1-9 ◽  
Author(s):  
H. Y. Lee ◽  
N. S. Jung ◽  
C. S. Ryoo
Keyword(s):  
Bernstein Polynomials ◽  
Genocchi Numbers

scholarly journals Novel Identities for -Genocchi Numbers and Polynomials

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Serkan Araci
Keyword(s):  
Bernstein Polynomials ◽  
Bernoulli Numbers ◽  
Genocchi Numbers

The essential aim of this paper is to introduce novel identities forq-Genocchi numbers and polynomials by using the method by T. Kim et al. (article in press). We show that these polynomials are related top-adic analogue of Bernstein polynomials. Also, we derive relations betweenq-Genocchi andq-Bernoulli numbers.

scholarly journals A Study on the Fermionic -Adic -Integral Representation on Associated with Weighted -Bernstein and -Genocchi Polynomials

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
Serkan Araci ◽  
Dilek Erdal ◽  
Jong Jin Seo
Keyword(s):  
Integral Representation ◽  
Bernstein Polynomials ◽  
Genocchi Numbers ◽  
Genocchi Polynomials

We consider weighted -Genocchi numbers and polynomials. We investigated some interesting properties of the weighted -Genocchi numbers related to weighted -Bernstein polynomials by using fermionic -adic integrals on .

scholarly journals Unified Degenerate Central Bell Polynomials

2019 ◽  
Author(s):  
Mehmet Acikgoz ◽  
Ugur Duran
Keyword(s):  
Explicit Formula ◽  
Bernstein Polynomials ◽  
Summation Formula ◽  
Bell Polynomials ◽  
Genocchi Numbers ◽  
Central Factorial Numbers ◽  
Degenerate Bernstein Polynomials

In this paper, we firstly consider extended degenerate central factorial numbers of the second kind and provide some properties of them. We then introduce unified degenerate central Bell polynomials and numbers and investigate many relations and formulas including summation formula, explicit formula and derivative property. Moreover, we derive several correlations for the fully degenerate central Bell polynomials associated with the degenerate Bernstein polynomials and the degenerate Bernoulli, Euler and Genocchi numbers.

scholarly journals Some Identities on the Twisted -Genocchi Numbers and Polynomials Associated with -Bernstein Polynomials

2011 ◽  
Vol 2011 ◽  
pp. 1-8 ◽  
Author(s):  
Seog-Hoon Rim ◽  
Sun-Jung Lee
Keyword(s):  
Bernstein Polynomials ◽  
Genocchi Numbers

We give some interesting identities on the twisted ()-Genocchi numbers and polynomials associated with -Bernstein polynomials.

scholarly journals Numerical Analysis of Viscoelastic Rotating Beam with Variable Fractional Order Model Using Shifted Bernstein–Legendre Polynomial Collocation Algorithm

2021 ◽  
Vol 5 (1) ◽  
pp. 8
Author(s):  
Cundi Han ◽  
Yiming Chen ◽  
Da-Yan Liu ◽  
Driss Boutat
Keyword(s):  
Numerical Analysis ◽  
Fractional Order ◽  
Governing Equation ◽  
Numerical Solutions ◽  
Bernstein Polynomials ◽  
Matrix Product ◽  
Algebraic Equations ◽  
Rotating Beam ◽  
The Matrix ◽  
The Time Domain

This paper applies a numerical method of polynomial function approximation to the numerical analysis of variable fractional order viscoelastic rotating beam. First, the governing equation of the viscoelastic rotating beam is established based on the variable fractional model of the viscoelastic material. Second, shifted Bernstein polynomials and Legendre polynomials are used as basis functions to approximate the governing equation and the original equation is converted to matrix product form. Based on the configuration method, the matrix equation is further transformed into algebraic equations and numerical solutions of the governing equation are obtained directly in the time domain. Finally, the efficiency of the proposed algorithm is proved by analyzing the numerical solutions of the displacement of rotating beam under different loads.

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