q-Poisson, q-Dobinski, q-Rota and q-coherent states
A. K.Kwasniewski
TL;DR
This paper explores q-analogues of classical combinatorial and probabilistic concepts, focusing on q-Poisson, q-Dobinski, q-Rota, and q-coherent states, connecting them through the interpretation of the q-Dobinski formula.
Contribution
It introduces and analyzes q-analogues of well-known formulas and states, providing new insights into their probabilistic and combinatorial interpretations.
Findings
q-Dobinski formula interpreted as average of powers of X_q
Connections established between q-Poisson distribution and q-coherent states
New properties of q-Rota and q-coherent states derived
Abstract
q- Dobinski formula may be interpreted as the average of powers of a random variable X_q with the q- Poisson distribution.
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Taxonomy
TopicsAdvanced Mathematical Identities · Mathematical functions and polynomials · Random Matrices and Applications