Abstract
A systemic study of some families of -Genocchi numbers and families of polynomials of Nörlund type is presented by using the multivariate fermionic -adic integral on . The study of these higher-order -Genocchi numbers and polynomials yields an interesting -analog of identities for Stirling numbers.
Highlights
Let p be a fixed odd prime number
Throughout this paper, Zp, Qp, C, and Cp denote the ring of p-adic rational integers, the field of p-adic rational numbers, the complex number field, and the completion of the algebraic closure of Qp, respectively
Let N be the set of natural numbers and Z p−vp p 1/p
Summary
Let p be a fixed odd prime number. Throughout this paper, Zp, Qp, C, and Cp denote the ring of p-adic rational integers, the field of p-adic rational numbers, the complex number field, and the completion of the algebraic closure of Qp, respectively. Let N be the set of natural numbers and Z p−vp p 1/p. When one talks of q-extension, q is variously considered as an indeterminate, a complex q ∈ C, or a p-adic number q ∈ Cp. If q ∈ C, one normally assumes |q| < 1. If q ∈ Cp, we assume |q − 1|p < 1. We use the following notation: xq 1 − qx 1−q.
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