-Genocchi Polynomials and Numbers of Higher Order
نویسندگان
چکیده
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.
منابع مشابه
NOTE ON THE GENERALIZATION OF THE HIGHER ORDER q-GENOCCHI NUMBERS AND q-EULER NUMBERS
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 ...
متن کاملOn 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 کاملOn the Twisted q-Genocchi Numbers and Polynomials with Weak Weight α
In this paper we construct a new type of twisted q-Genocchi numbers and polynomials with weak weight α. We investigate some properties which are related to twisted q-Genocchi numbers G (α) n,q,w and polynomials G (α) n,q,w (x) with weak weight α. Keywords: Genocchi numbers and polynomials, twisted q-Genocchi numbers and polynomials, twisted q-Genocchi numbers and polynomials with weak weight α
متن کاملOn Some Arithmetical Properties of the Genocchi Numbers and Polynomials
We investigate the properties of the Genocchi functions and the Genocchi polynomials. We obtain the Fourier transform on the Genocchi function.We have the generating function of h, q -Genocchi polynomials. We define the Cangul-Ozden-Simsek’s type twisted h, q -Genocchi polynomials and numbers. We also have the generalized twisted h, q -Genocchi numbers attached to the Dirichlet’s character χ. F...
متن کاملAlgorithms for Bernoulli and Allied Polynomials
We investigate some algorithms that produce Bernoulli, Euler and Genocchi polynomials. We also give closed formulas for Bernoulli, Euler and Genocchi polynomials in terms of weighted Stirling numbers of the second kind, which are extensions of known formulas for Bernoulli, Euler and Genocchi numbers involving Stirling numbers of the second kind.
متن کامل