On the Higher-Order q-Euler Numbers and Polynomials with Weight α
نویسندگان
چکیده
Let p be a fixed odd prime. Throughout this paper Zp,Qp,C, andCp, will, respectively, denote the ring of p-adic rational integers, the field, of p-adic rational numbers, the complex number field and the completion of algebraic closure of Qp. Let N be the set of natural numbers and Z N ∪ {0}. Let νp be the normalized exponential valuation of Cp with |p|p p−νp p p−1 see 1–14 . When one speaks of q-extension, q can be regarded as an indeterminate, complex number q ∈ C, or p-adic number q ∈ Cp; it is always clear from context. If q ∈ C, we assume |q| < 1. If q ∈ Cp, then we assume |1 − q|p < 1 see 1–14 . In this paper, we use the notation of q-number as follows:
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