Abstract
In this paper, we study some interesting identities of Frobenius-Euler polynomials arising from umbral calculus.
Highlights
Let C be the complex number field, and let F be the set of all formal power series in the variable t over C with F= f (t) = ∞ ak tk k! ak ∈C k=We use notation P = C[x] and P* denotes the vector space of all linear functional on P
We study some interesting identities of Frobenius-Euler polynomials arising from umbral calculus
1 Introduction Let C be the complex number field, and let F be the set of all formal power series in the variable t over C with
Summary
Let C be the complex number field, and let F be the set of all formal power series in the variable t over C with. We use notation P = C[x] and P* denotes the vector space of all linear functional on P. L|p(x) denotes the action of the linear functional L on the polynomial p(x), and we remind that the vector space operations on P* is defined by. For y in C the evaluation functional is defined to be the power series eyt. For λ (= ) ∈ C, we recall that the Frobenius-Euler polynomials are defined by the generating function to be. Hk+ (x + |λ) – λHk+ (x|λ) = (x + )Hk(x + |λ) – λxHk(x|λ) – Hk(x + |λ) = xHk(x + |λ) – λxHk(x|λ). By ( ), we obtain the following theorem. Let P(λ) = {p(x) ∈ Q(λ)[x]| deg p(x) ≤ n} be a vector space over Q(λ).
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