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Study on r-truncated degenerate Stirling numbers of the second kind

Study on \(r\)-truncated degenerate Stirling numbers of the second kind
Authors: Kim Taekyun; Kim Dae San; Kim Hyekyung;

Study on r-truncated degenerate Stirling numbers of the second kind

Abstract

Abstract The degenerate Stirling numbers of the second kind and of the first kind, which are, respectively, degenerate versions of the Stirling numbers of the second kind and of the first kind, appear frequently when we study various degenerate versions of some special numbers and polynomials. The aim of this article is to consider the r-truncated degenerate Stirling numbers of the second kind, which reduce to the degenerate Stirling numbers of the second for r = 1, and to investigate their explicit expressions, some properties and related identities, in connection with several other degenerate special numbers and polynomials.

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Keywords

Mathematics - Number Theory, Bell and Stirling numbers, r-truncated degenerate stirling numbers of the second kind, \(r\)-truncated degenerate Bernoulli polynomials of order alpha, 11b83, 11b73, \(r\)-truncated degenerate Stirling numbers of the second kind, QA1-939, FOS: Mathematics, Number Theory (math.NT), 11B73, 11B83, Bernoulli and Euler numbers and polynomials, r-truncated degenerate bernoulli polynomials of order alpha, Mathematics

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
5
Top 10%
Average
Top 10%
Green
gold