منابع مشابه
Interpolation Functions of q-Extensions of Apostol's Type Euler Polynomials
The main purpose of this paper is to present new q-extensions of Apostol’s type Euler polynomials using the fermionic p-adic integral on Zp. We define the q-λ-Euler polynomials and obtain the interpolation functions and the Hurwitz type zeta functions of these polynomials. We define qextensions of Apostol type’s Euler polynomials of higher order using the multivariate fermionic p-adic integral ...
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and Applied Analysis 3 Remark 1.2. In 1.6 ; we easily see that lim q→ 1 F r q t, x 2 ∞ ∑ m 0 −1 m ( m r − 1 m ) e m x t 2e ∞ ∑ m 0 −1 m ( m r − 1 m ) e 2e 1 et r F r t, x . 1.7 From the above, we obtain generating function of the Nörlund Euler numbers of higher order. That is F r t, x 2e 1 et r ∞ ∑ n 0 E r n x t n! . 1.8 Thus, we have lim q→ 1 E r n,q x E r n x . 1.9 cf. 21 . Hence, we have F r...
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In this work, by using a p-adic q-Volkenborn integral, we construct a new approach to generating functions of the (h, q)-Euler numbers and polynomials attached to a Dirichlet character χ . By applying the Mellin transformation and a derivative operator to these functions, we define (h, q)-extensions of zeta functions and l-functions, which interpolate (h, q)-extensions of Euler numbers at negat...
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The aim of this paper is to construct p-adic twisted two-variable Eulerh,q -L-functions, which interpolate generalized twisted h,q -Euler polynomials at negative integers. In this paper, we treat twisted h,q -Euler numbers and polynomials associated with p-adic invariant integral on Zp. We will construct two-variable twisted h,q -Euler-zeta function and two-variable h,q -L-function in Complex s...
متن کاملApostol-euler Polynomials of Higher Order and Gaussian Hypergeometric Functions
The purpose of this paper is to give analogous definitions of Apostol type (see T. M. Apostol [Pacific J. Math. 1 (1951), 161-167]) for the so-called Apostol-Euler numbers and polynomials of higher order. We establish their elementary properties, obtain several explicit formulas involving the Gaussian hypergeometric function and the Stirling numbers of the second kind, and deduce their special ...
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ژورنال
عنوان ژورنال: Journal of Inequalities and Applications
سال: 2009
ISSN: 1029-242X
DOI: 10.1155/2009/451217