Degenerate r-Whitney numbers and degenerate r-Dowling polynomials via boson operators

Dowling showed that the Whitney numbers of first kind and second satisfy Stirling number-like relations. Recently, Kim-Kim introduced degenerate r-Whitney kind, as versions further generalizations both kinds. The normal ordering an integral power number operator in terms boson operators is expressed with help kind. In this paper, it noted a certain quantity involving We derive some properties, recurrence relations, orthogonality relations several identities on those from such ordering. addition, we consider r-Dowling polynomials natural extension investigate their properties.