scholarly journals Matrix approach to hypercomplex Appell polynomials

2017 ◽  
Vol 116 ◽  
pp. 2-9 ◽  
Author(s):  
Lidia Aceto ◽  
Helmut Robert Malonek ◽  
Graça Tomaz
Keyword(s):  
Matrix Approach ◽  
Appell Polynomials

scholarly journals -Pascal and -Wronskian Matrices with Implications to -Appell Polynomials

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Thomas Ernst
Keyword(s):  
Difference Equation ◽  
Recent Article ◽  
Matrix Multiplication ◽  
Euler Polynomials ◽  
Matrix Approach ◽  
Appell Polynomials ◽  
Sum Of Products ◽  
Functional Matrix

We introduce a -deformation of the Yang and Youn matrix approach for Appell polynomials. This will lead to a powerful machinery for producing new and old formulas for -Appell polynomials, and in particular for -Bernoulli and -Euler polynomials. Furthermore, the --polynomial, anticipated by Ward, can be expressed as a sum of products of -Bernoulli and -Euler polynomials. The pseudo -Appell polynomials, which are first presented in this paper, enable multiple -analogues of the Yang and Youn formulas. The generalized -Pascal functional matrix, the -Wronskian vector of a function, and the vector of -Appell polynomials together with the -deformed matrix multiplication from the authors recent article are the main ingredients in the process. Beyond these results, we give a characterization of -Appell numbers, improving on Al-Salam 1967. Finally, we find a -difference equation for the -Appell polynomial of degree .

scholarly journals A unified matrix approach to the representation of Appell polynomials

2015 ◽  
Vol 26 (6) ◽  
pp. 426-441 ◽  
Author(s):  
L. Aceto ◽  
H.R. Malonek ◽  
G. Tomaz
Keyword(s):  
Matrix Approach ◽  
Appell Polynomials
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