Abstract
The purpose of this paper is to give some properties of several Bernstein type polynomials to represent the fermionic -adic integral on . From these properties, we derive some interesting identities on the Euler numbers and polynomials.
Highlights
É Throughout this paper, let p be an odd prime number
We study the properties of Bernstein polynomials in the p-adic number field
For f ∈ UD p, we give some properties of several type Bernstein polynomials to represent the fermionic p-adic invariant integral on p
Summary
É Throughout this paper, let p be an odd prime number. The symbol, p, p , and p denote the ring of p-adic integers, the field of p-adic rational numbers, the complex number field and the completion of algebraic closure of Ép , respectively. For f ∈ UD p , the fermionic p-adic q-integral on p is defined as I−1 f f x dμ−1 x , 1.2 p is called the fermionic p-adic invariant integral on p see 2 .
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