Applied Mathematics in Science and Engineering (Dec 2022)

Normal ordering of degenerate integral powers of number operator and its applications

  • Taekyun Kim,
  • Dae San Kim,
  • Hye Kyung Kim

DOI
https://doi.org/10.1080/27690911.2022.2083120
Journal volume & issue
Vol. 30, no. 1
pp. 440 – 447

Abstract

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The normal ordering of an integral power of the number operator in terms of boson operators is expressed with the help of the Stirling numbers of the second kind. As a ‘degenerate version’ of this, we consider the normal ordering of a degenerate integral power of the number operator in terms of boson operators, which is represented by means of the degenerate Stirling numbers of the second kind. As an application of this normal ordering, we derive two equations defining the degenerate Stirling numbers of the second kind and a Dobinski-like formula for the degenerate Bell polynomials.

Keywords