On the Generalized q-Genocchi Numbers and Polynomials of Higher-Order
نویسندگان
چکیده
منابع مشابه
On the Generalized q-Genocchi Numbers and Polynomials of Higher-Order
where we use the technical method’s notation by replacing G x by Gn x , symbolically, see 1, 2 . In the special case x 0, Gn Gn 0 are called the nth Genocchi numbers. From the definition of Genocchi numbers, we note that G1 1, G3 G5 G7 · · · 0, and even coefficients are given by G2n 2 1 − 22n B2n 2nE2n−1 0 see 3 , where Bn is a Bernoulli number and En x is an Euler polynomial. The first few Gen...
متن کامل-Genocchi Polynomials and Numbers of Higher Order
Copyright q 2010 Lee-Chae Jang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We investigate several arithmetic properties of h, q-Genocchi polynomials and numbers of higher order.
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Cangul-Ozden-Simsek[1] constructed the q-Genocchi numbers of high order using a fermionic p-adic integral on Zp, and gave Witt’s formula and the interpolation functions of these numbers. In this paper, we present the generalization of the higher order q-Euler numbers and q-Genocchi numbers of Cangul-Ozden-Simsek. We define q-extensions of w-Euler numbers and polynomials, and w-Genocchi numbers ...
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have numerous important applications in number theory, combinatorics, and numerical analysis, among other areas, [1–13]. It is easy to find the values G1 = 1, G3 = G5 = G7 = ··· = 0, and even coefficients are given by G2m = 2(1− 2)B2n = 2nE2n−1(0), where Bn is a Bernoulli number and En(x) is an Euler polynomial. The first few Genocchi numbers for n= 2,4, . . . are −1,−3,17,−155,2073, . . . . Th...
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Let p be an odd prime number. For n ∈ Z N ∪ {0}, let Cpn {ζ | ζpn 1} be the cyclic group of order p, and let Tp limn→∞Cpn ⋃ n≥0 Cpn Cp∞ be the space of locally constant functions in the p-adic number fieldCp. When one talks of q-extension, q is variously considered as an indeterminate, a complex number q ∈ C, or p-adic number q ∈ Cp. If q ∈ C, one normally assumes that |q| < 1. If q ∈ Cp, one n...
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ژورنال
عنوان ژورنال: Advances in Difference Equations
سال: 2011
ISSN: 1687-1839,1687-1847
DOI: 10.1155/2011/424809