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arXiv.org e-Print Archive
Preprint . 2004
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$\psi$-Poisson, $q$-Cigler, $\psi$-Dobinski, $\psi$-Rota and $\psi$-coherent states

descriptionPublicationkeyboard_double_arrow_right Preprint 02 Mar 2004
Authors: Kwasniewski, A. K.;

arXiv: math/0403054

$\psi$-Poisson, $q$-Cigler, $\psi$-Dobinski, $\psi$-Rota and $\psi$-coherent states

Abstract

Cigler simple derivation of usual and extended Dobinski formula is recalled and it is noted that both may be interpreted as averages of powers of random variables with the corresponding usual or extended Poisson distributions. In parallel more general formulas of extended operator umbral calculi origin are revealed . The formulas encompass both earlier cases as very specific ones.

Comment: 6 pages

Keywords

Mathematics - Combinatorics, 05A40, 81S99, Computer Science - Discrete Mathematics

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
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