Generalized degenerate stirling numbers arising from degenerate boson normal ordering

TL;DR

This paper introduces generalized degenerate (r, s)-Stirling numbers and Bell polynomials derived from degenerate boson normal ordering, providing new properties, explicit formulas, and generating functions for these mathematical objects.

Contribution

It extends the theory of degenerate special numbers by defining and analyzing generalized degenerate (r, s)-Stirling numbers and Bell polynomials related to boson normal ordering.

Findings

Derived properties and explicit formulas for the numbers and polynomials.

Established generating functions for the generalized degenerate (r, s)-Stirling numbers.

Connected the new concepts to existing generalized Stirling numbers and boson normal ordering.

Abstract

It is remarkable that, in recent years, intensive studies have been done for degenerate versions of many special polynomials and numbers and have yielded many interesting results. The aim of this paper is to study the generalized degenerate (r, s)-Stirling numbers of the second and their natural extensions to polynomials, namely the generalized degenerate (r, s)-Bell polynomials, arising from certain degenerate boson normal ordering. We derive some properties, explicit expressions and generating functions for those numbers and polynomials. The generalized degenerate (r, s)-Stirling numbers of the second and the degenerate boson normal ordering are respectively degenerate versions of the generalized (r, s)-Stirling numbers of the second and the boson normal ordering studied earlier by Blasiak-Person-Solomon.