2002/11/06 by K. A. Penson, Karol A. Penson, Penson, Karol A. +2
Chemistry · Mathematics · Physics and Astronomy · #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Molecular spectroscopy and chirality #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #math.CO #quant-ph
paper · pdf · doi:10.48550/arxiv.quant-ph/0211028
4 pages. Proceedings of Group 24, Paris, July 2002
arxiv created 2002/11/06 · openalex publication_date 2002/11/06 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We derive explicit formulas for the normal ordering of powers of arbitrary monomials of boson operators. These formulas lead to generalisations of conventional Bell and Stirling numbers and to appropriate generalisations of the Dobinski relations. These new combinatorial numbers are shown to be coherent state matrix elements of powers of the monomials in question. It is further demonstrated that such Bell-type numbers, when considered as power moments, give rise to positive measures on the positive half-axis, which in many cases can be written in terms of known functions.