Information on some recent applications of umbral extensions to discrete mathematics
نویسنده
چکیده
At the first part of our communicate we show how specific umbral extensions of the Stirling numbers of the second kind result in new type of Dobinski-like formulas. In the second part among others one recovers how and why Morgan Ward solution of uncountable family of ψ-difference calculus nonhomogeneous equations ∆ ψ f = ϕ in the form f (x) = n≥1 B n n ψ ! ϕ (n−1) (x) + ψ ϕ(x) + p(x) extends to ψ-Appell polynomials case automatically. Illustrative specifications to q-calculus case and Fibonomial calculus case are made explicit due to the usage of upside down notation for objects of Extended Finite Operator Calculus .
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N ov 2 00 4 Information on some recent applications of umbral extensions to discrete mathematics
At the first part of our communicate we show how specific umbral extensions of the Stirling numbers of the second kind result in new type of Dobinski-like formulas. In the second part among others one recovers how and why Morgan Ward solution of uncountable family of ψ-difference calculus nonhomogeneous equations ∆ ψ f = ϕ in the form f (x) = n≥1 B n n ψ ! ϕ (n−1) (x) + ψ ϕ(x) + p(x) extends to...
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