A Note on (h,q)-Genocchi Polynomials and Numbers of Higher Order

Abstract

We investigate several arithmetic properties of h, q-Genocchi polynomials and numbers of higher order.

A Note on the p-Adic Interpolation Function for Multiple Generalized Genocchi Numbers

“…Taking x = 0 in (1.2), then we have G For f ∈ N with f ≡ 1 (mod 2), we assume that χ is a primitive Dirichlet's charachter with conductor f . It is known in [28] that the Genocchi numbers associated with χ, G n,χ , was introduced by the following expression…”

A family of generalized q-Genocchi numbers and polynomials

“…where we use the technical method's notation by replacing G n (x) by G n (x), symbolically, (see [3,11]).…”

“…In the special case x = 0, G n,χ = G n,χ (0) are called the n-th generalized Genocchi numbers attached to χ (see [3,4,5,6]). For a real or complex parameter α, the generalized higher-order Genocchi polynomials attached to χ are also defined by…”

“…n,χ (0) are called the n-th generalized Genocchi numbers attached to χ of order α (see [3,4,5,6,13,14,15]). From (3) and (4), we derive G n,χ = G (1) n,χ .…”

“…Spherical functions on quantum groups are q-special functions. Recently, many authors have studied the qextension in various area( see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]). Govil and Gupta [2] has introduced a new type of q-integrated Meyer-König-Zeller-Durrmeyer operators and their results are closely related to study q-Bernstein polynomials and q-Genocchi polynomials, which are treated in this paper.…”