Dual Numbers and Operational Umbral Methods
نویسندگان
چکیده
منابع مشابه
Umbral Methods, Combinatorial Identities and Harmonic Numbers
We analyse and demonstrate how umbral methods can be applied for the study of the problems, involving combinatorial calculus and harmonic numbers. We demonstrate their efficiency and we find the general procedure to frame new and existent identities within a unified framework, amenable of further generalizations.
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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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In this paper, we give some interesting identities of poly-Cauchy numbers and polynomials arising from umbral calculus.
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We use the viewpoint of the formal calculus underlying vertex operator algebra theory to study certain aspects of the classical umbral calculus. We begin by calculating the exponential generating function of the higher derivatives of a composite function, following a very short proof which naturally arose as a motivating computation related to a certain crucial “associativity” property of an im...
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ژورنال
عنوان ژورنال: Axioms
سال: 2019
ISSN: 2075-1680
DOI: 10.3390/axioms8030077