Abstract
The aim of this paper is to prove multiplication formulas of the normalized polynomials by using the umbral algebra and umbral calculus methods. Our polynomials are related to the Hermite-type polynomials.
Highlights
In this paper, we use the following notations:N := {, . . .} and ⎧ ⎨ δn,k = ⎩if n = k, if n = k, N := N ∪ { },(n)k = n(n – ) · · · (n – k + ).Here, we first give some remarks on the normalized polynomials
For q = pn, we denote by Fq the finite field having q elements
We study normalized polynomials which are defined above by using the umbral algebra and umbral calculus methods
Summary
We first give some remarks on the normalized polynomials. Equation ( ) is satisfied by a unique set of normalized polynomials {fm(x)} which form an Appell set (cf [ ]). If fn(x) is a normalized polynomial, it satisfies the following formula: y– If y is an even positive integer, some normalized polynomials satisfy the following equation (cf [ ]): Where gn– (x) and fn(x) denote the normalized polynomials of degree n – and n, respectively.
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