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Fractional difference calculus. (English) Zbl 0693.39002
Univalent functions, fractional calculus, and their applications, 139-152 (1989).

[For the entire collection see Zbl 0683.00012.]

In 1886 Laurent treated the well-known formula (1)D n x λ =λ(λ-1)···(λ-n+1)x λ-n , where n is a positive integer, and defined the meaning of this formula (1) when n is not necessarily a positive integer. In the present paper the authors treat the well-known formula of difference operators (2)Δ n f(x)= k=0 n (-1) k nkf(x+n-k), where n is a positive integer, and define the meaning of (2) when n is not necessarily a positive integer. Furthermore, they derive some consequences of this definition and present its application.

Reviewer: H.Haruki
MSC:
39A70Difference operators
39A12Discrete version of topics in analysis
26A33Fractional derivatives and integrals (real functions)