Study on the some identities of degenerate Stirling numbers of the first kind and second kind

초록

In 1979, L. Carlitz introduced the degenerate Stirling, Bernoulli, and Eulerian numbers in Util. Math. Since then, degenerate versions of special polynomials and numbers have been introduced by many researchers, and the properties of these polynomials and numbers have been investigated. Kim and Kim defined the lambda-analogue of r-Stirling numbers of the second kind, and gave the recurrence relations for these numbers. The purpose of this paper is to derive some interesting identities related to the degenerate Stirling numbers of the first and second kind, degenerate r-Stirling numbers of the second kind, falling factorial sequences, harmonic numbers and Gindalrae-Stirling numbers of the first kind using binomial transform. Furthermore, the shape change of the degenerate r-Stirling number S(r) 2,lambda (k, n) with respect to lambda was demonstrated using Mathematica.

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