A Note on the Generalized Euler Numbers and Polynomials
نویسنده
چکیده
Let p be an odd prime number. Throughout this paper Zp, Qp, C, and Cp 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. The normalized valuation in Cp is denoted by | · |p with |p|p = 1 p . We say that f is a uniformly differentiable function at a point a ∈ Zp and denote this property by f ∈ UD(Zp), if the difference quotients Ff (x, y) = f(x)− f(y) x− y have a limit l = f (a) as (x, y) → (a, a). For f ∈ UD(Zp), let us start with the expression
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