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Characterization of various Appel polynomials sequences
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Abstract
In this paper, we characterize various sequences of the Appell polynomials by means of the formula of representation of powers viewed from a linear operator perspective. First we construct some Gauss-Weierstrass integral representation operators for various sequence of Appell polynomials such as Euler-Frobenius polynomials, Degenerate Bernoulli polynomials, Bell-Touchard polynomials and for the generalized Tempesta-Bernoulli polynomials. Secondly, we introduce the Appell polynomials as well as the Hurwitz zeta function as eigenfunctions (eigenvectors) of certain well chosen discrete version of Gauss-Weierstrass integral operators. Our approach is inspired by the Gauss-Weierstrass transform for Hermite polynomials.
Title: Characterization of various Appel polynomials sequences
Description:
Abstract
In this paper, we characterize various sequences of the Appell polynomials by means of the formula of representation of powers viewed from a linear operator perspective.
First we construct some Gauss-Weierstrass integral representation operators for various sequence of Appell polynomials such as Euler-Frobenius polynomials, Degenerate Bernoulli polynomials, Bell-Touchard polynomials and for the generalized Tempesta-Bernoulli polynomials.
Secondly, we introduce the Appell polynomials as well as the Hurwitz zeta function as eigenfunctions (eigenvectors) of certain well chosen discrete version of Gauss-Weierstrass integral operators.
Our approach is inspired by the Gauss-Weierstrass transform for Hermite polynomials.
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