Abstract
In this paper, we study some p-adic Frobenius-Euler measure related to umbral calculus in the p-adic case. Finally, we derive some identities of Frobenius-Euler polynomials from our study.MSC:05A10, 05A19.
Highlights
For k ≥ and λ ∈ Cp with | – λ|p >, the Frobenius-Euler measure on X is defined by μλ x + fpN Zp λfpN –x = – λfpN
For r ∈ N, the Frobenius-Euler polynomials of order r are defined by the generating function
In [ ], Kim and Kim have studied some identities of Frobenius-Euler polynomials arising from umbral calculus
Summary
For k ≥ and λ ∈ Cp with | – λ|p > , the Frobenius-Euler measure on X is defined by μλ x + fpN Zp λfpN –x = – λfpN The Frobenius-Euler polynomials are defined by the generating function to be X = , Hn( |λ) = Hn(λ) are called the nth Frobenius-Euler numbers For r ∈ N, the Frobenius-Euler polynomials of order r are defined by the generating function
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