THE FERMIONIC p-ADIC INTEGRALS ON Zp ASSOCIATED WITH EXTENDED q-EULER NUMBERS AND POLYNOMIALS
نویسنده
چکیده
Let p be a fixed odd prime number. Throughout this paper Zp, Qp, C and Cp will, respectively, denote the ring of p-adic rational integers, the field of p-adic rational numbers, the complex number field and the completion of algebraic closure of Qp. Let vp be the normalized exponential valuation of Cp with |p|p = p −vp(p) = 1 p . When one talks of q-extension, q is variously considered as and indeterminate, a complex number q ∈ C or p-adic number q ∈ Cp. If q ∈ C, one normally assumes |q| < 1. If q ∈ Cp, one normally assumes |1− q|p < 1. We use the notation
منابع مشابه
AN IDENTITY OF THE SYMMETRY FOR THE FROBENIUS-EULER POLYNOMIALS ASSOCIATED WITH THE FERMIONIC p-ADIC INVARIANT q-INTEGRALS ON Zp
Abstract. The main purpose of this paper is to prove an identity of symmetry for the Frobenius-Euler polynomials. It turns out that the recurrence relation and multiplication theorem for the Frobenius-Euler polynomials which discussed in [ K. Shiratani, S. Yamamoto, On a p-adic interpolation function for the Euler numbers and its derivatives, Memo. Fac. Sci. Kyushu University Ser.A, 39(1985), 1...
متن کاملJ ul 2 00 6 ON THE ANALOGS OF EULER NUMBERS AND POLYNOMIALS ASSOCIATED WITH
Abstract. The purpose of this paper is to construct of λ-Euler numbers and polynomials by using fermionic expression of p-adic q-integral at q = −1. From these λ-Euler polynomials, we derive the harmonic sums of higher order. Finally, we investigate several interesting properties and relationships involving the classical as well as the generalized Euler numbers and polynomials. As an applicatio...
متن کاملOn q-Euler Numbers Related to the Modified q-Bernstein Polynomials
and Applied Analysis 3 see 8 . For 0 ≤ k ≤ n, derivatives of the nth degree modified q-Bernstein polynomials are polynomials of degree n − 1: d dx Bk,n ( x, q ) n ( qBk−1,n−1 ( x, q ) − q1−xBk,n−1 ( x, q )) ln q q − 1 1.9 see 8 . The Bernstein polynomials can also be defined in many different ways. Thus, recently, many applications of these polynomials have been looked for by many authors. In t...
متن کاملA Note on the Generalized q - Euler Numbers and Polynomials with Weak Weight α
Many mathematicians have studied Euler numbers and Euler polynomials( see [1-11]). Euler polynomials posses many interesting properties and arising in many areas of mathematics and physics. In this paper we introduce the generalized q-Euler numbers and polynomials with weak weight α. Throughout this paper we use the following notations. By Zp we denote the ring of p-adic rational integers, Q de...
متن کاملNote on q-Extensions of Euler Numbers and Polynomials of Higher Order
In [14] Ozden-Simsek-Cangul constructed generating functions of higher-order twisted (h, q)-extension of Euler polynomials and numbers, by using p-adic q-deformed fermionic integral on Zp. By applying their generating functions, they derived the complete sums of products of the twisted (h, q)-extension of Euler polynomials and numbers, see[13, 14]. In this paper we cosider the new q-extension o...
متن کامل