J ul 2 00 6 ON THE ANALOGS OF EULER NUMBERS AND POLYNOMIALS ASSOCIATED WITH
نویسنده
چکیده
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 application, we will treat p-adic invariant integrals on Zp involving trigonometric functions.
منابع مشابه
Research Article Some Relationships between the Analogs of Euler Numbers and Polynomials
We construct new twisted Euler polynomials and numbers. We also study the generating functions of the twisted Euler numbers and polynomials associated with their interpolation functions. Next we construct twisted Euler zeta function, twisted Hurwitz zeta function, twisted Dirichlet l-Euler numbers and twisted Euler polynomials at non-positive integers, respectively. Furthermore, we find distrib...
متن کاملViewing Some Ordinary Differential Equations from the Angle of Derivative Polynomials
In the paper, the authors view some ordinary differential equations and their solutions from the angle of (the generalized) derivative polynomials and simplify some known identities for the Bernoulli numbers and polynomials, the Frobenius-Euler polynomials, the Euler numbers and polynomials, in terms of the Stirling numbers of the first and second kinds.
متن کامل2 00 9 A note on the generalized q - Euler numbers
Recently the new q-Euler numbers and polynomials related to Frobenius-Euler numbers and polynomials are constructed by Kim (see[3]). In this paper, we study the generalized q-Euler numbers and polynomials attached to χ related to the new q-Euler numbers and polynomials which is constructed in [3]. Finally, we will derive some interesting congruence on the generalized q-Euler numbers and polynom...
متن کاملq-Analogs of Classical 6-Periodicity: From Euler to Chebyshev
q-Analogs of Classical 6-Periodicity: From Euler to Chebyshev Boris A KUPERSHMIDT The University of Tennessee Space Institute, Tullahoma, TN 37388, USA E-mail: [email protected] Received November 19, 2002; Accepted January 03, 2003 Abstract The sequence of period 6 starting with 1, 1, 0,−1,−1, 0 appears in many different disguises in mathematics. Various q-versions of this sequence are found, a...
متن کاملEnumeration of snakes and cycle-alternating permutations
Springer numbers are analogs of Euler numbers for the group of signed permutations. Arnol’d showed that they count some objects called snakes, which generalize alternating permutations. Hoffman established a link between Springer numbers, snakes, and some polynomials related with the successive derivatives of trigonometric functions. The goal of this article is to give further combinatorial pro...
متن کامل