Balance Control of the Pendubot via the Polynomial Matrix Approach

2018 ◽  
Author(s):  
Antonis Vardulakis ◽  
Cui Wei
Keyword(s):  
Polynomial Matrix ◽  
Balance Control ◽  
Matrix Approach

scholarly journals New Generalized Apostol-Frobenius-Euler polynomials and their Matrix Approach

2021 ◽  
Vol 45 (03) ◽  
pp. 393-407
Author(s):  
MARÍA JOSÉ ORTEGA ◽  
WILLIAM RAMÍREZ ◽  
ALEJANDRO URIELES
Keyword(s):  
Polynomial Matrix ◽  
Product Formula ◽  
Euler Polynomial ◽  
Euler Polynomials ◽  
Matrix Approach ◽  
Pascal Matrix ◽  
Differential Properties ◽  
Euler Matrix

In this paper, we introduce a new extension of the generalized Apostol-Frobenius-Euler polynomials ℋn[m−1,α](x; c,a; λ; u). We give some algebraic and differential properties, as well as, relationships between this polynomials class with other polynomials and numbers. We also, introduce the generalized Apostol-Frobenius-Euler polynomials matrix ????[m−1,α](x; c,a; λ; u) and the new generalized Apostol-Frobenius-Euler matrix ????[m−1,α](c,a; λ; u), we deduce a product formula for ????[m−1,α](x; c,a; λ; u) and provide some factorizations of the Apostol-Frobenius-Euler polynomial matrix ????[m−1,α](x; c,a; λ; u), which involving the generalized Pascal matrix.

Sign in / Sign up

Export Citation Format

Share Document