$ψ$-Poisson, $q$-Cigler, $ψ$-Dobinski, $ψ$-Rota and $ψ$-coherent states

Details $ψ$-Poisson, $q$-Cigler, $ψ$-Dobinski, $ψ$-Rota and $ψ$-coherent states $ψ$-Poisson, $q$-Cigler, $ψ$-Dobinski, $ψ$-Rota and $ψ$-coherent states

2004-03-02

arxiv.org/abs/math/0403054v1

Proc. Jangjeon Math. Soc. Vol. 7 (2), 2004 pp. 95-98

Mathematics

Combinatorics

6 pages

Scientific paper

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.

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