AN IDENTITY OF THE SYMMETRY FOR THE FROBENIUS-EULER POLYNOMIALS ASSOCIATED WITH THE FERMIONIC p-ADIC INVARIANT q-INTEGRALS ON Zp

نویسنده

  • Taekyun Kim
چکیده

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), 113-125]. Finally we investigate several further interesting properties of symmetry for the fermionic p-adic invariant q-integral on Zp associated with the Frobenius-Euler polynomials and numbers.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

J 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 کامل

On 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 کامل

On the Identities of Symmetry for the ζ-Euler Polynomials of Higher Order

The main purpose of this paper is to investigate several further interesting properties of symmetry for the multivariate p-adic fermionic integral on Zp. From these symmetries, we can derive some recurrence identities for the ζ-Euler polynomials of higher order, which are closely related to the Frobenius-Euler polynomials of higher order. By using our identities of symmetry for the ζEuler polyn...

متن کامل

Symmetry Fermionic p-Adic q-Integral on ℤp for Eulerian Polynomials

Kim et al. 2012 introduced an interesting p-adic analogue of the Eulerian polynomials. They studied some identities on the Eulerian polynomials in connection with the Genocchi, Euler, and tangent numbers. In this paper, by applying the symmetry of the fermionic p-adic q-integral on Zp, defined by Kim 2008 , we show a symmetric relation between the q-extension of the alternating sum of integer p...

متن کامل

An Identity of the Generalized q-Euler Polynomials with Weak Weight α Associated with p-Adic Invariant q-Integral on Zp

Throughout this paper we use the following notations. By Zp we denote the ring of p-adic rational integers, Q denotes the field of rational numbers, Qp denotes the field of p-adic rational numbers, C denotes the complex number field, and Cp denotes the completion of algebraic closure of Qp. Let νp be the normalized exponential valuation of Cp with |p|p = p−νp(p) = p−1. When one talks of q-exten...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2008