Abstract
In the present paper, we introduce Eulerian polynomials attached to by using p-adic q-integral on Zp . Also, we give new interesting identities via the generating functions of Dirichlet's type of Eulerian polynomials. After, by applying Mellin transformation to this generating function of Dirichlet' type of Eulerian polynomials, we derive L-function for Eulerian polynomials which interpolates of Dirichlet's type of Eulerian polynomials at negative integers.
Highlights
In the present paper, we introduce the Eulerian polynomials attached to v using p-adic q-integral on Zp
Kim et al have studied on the Eulerian polynomials and derived Witt’s formula for the Eulerian polynomials together with the relations between Genocchi, Tangent and Euler numbers
The Eulerian polynomials can be generated via the recurrence relation:
Summary
Kim et al have studied on the Eulerian polynomials and derived Witt’s formula for the Eulerian polynomials together with the relations between Genocchi, Tangent and Euler numbers. For more on this and related issues, see, e.g., [1]. M. Srivastava and other related mathematicians, they have introduced many various generating functions for types of the Bernoulli, the Euler, the Genocchi numbers and polynomials and derived some new interesting identities (see [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28] for a systematic work). We briefly summarize some properties of the usual Eulerian polynomials: The Eulerian polynomials AnðxÞ are defined as (known as the generating function of Eulerian poynomials) eAðxÞt
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