New formulas for Stirling-like numbers and Dobinski-like formulas
نویسنده
چکیده
Extensions of the Stirling numbers of the second kind and Dobinski-like formulas are proposed in a series of exercises for graduetes. Some of these new formulas recently discovered by me are to be found in A.K.Kwaśniewski’s source paper [1]. These extensions naturally encompass the well known q-extensions.The indicatory references are to point at a part of the vast domain of the foundations of computer science in ArXiv affiliation noted as CO.cs.DM. MCS numbers: 05A40, 11B73, 81S99
منابع مشابه
On umbral extensions of Stirling numbers and Dobinski-like formulas
ψ-umbral extensions of the Stirling numbers of the second kind are considered and the resulting new type of Dobinski-like formulas are discovered. These extensions naturally encompass the two well known q-extensions .The further consecutive ψ-umbral extensions of CarlitzGould q-Stirling numbers are therefore realized here in a two-fold way . The fact that the umbral q-extended Dobinski formula ...
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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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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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ورودعنوان ژورنال:
- CoRR
دوره abs/0803.1416 شماره
صفحات -
تاریخ انتشار 2008