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Some Properties of Associated Stirling Numbers

Feng-Zhen Zhao

Open publisher page 9 citations

Abstract

In this paper, we discuss the properties of associated Stirling numbers. By means of the method of coefficients, we establish a series of identities involving associated Stirling numbers, Bernoulli numbers, harmonic numbers, and the Cauchy numbers of the first kind. In addition, we give the asymptotic expansion of certain sums involving 2-associated Stirling numbers of the second kind by Darboux’s method.

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What this paper is about

In this paper, we discuss the properties of associated Stirling numbers. By means of the method of coefficients, we establish a series of identities involving associated Stirling numbers, Bernoulli numbers, harmonic numbers, and the Cauchy numbers of the first kind. In addition, we give the asymptotic expansion of certain sums involving 2-associated Stirling numbers of the second kind by Darboux’s method.

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OpenAlex reports 9 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

In this paper, we discuss the properties of associated Stirling numbers. By means of the method of coefficients, we establish a series of identities involving associated Stirling numbers, Bernoulli numbers, harmonic numbers, and the Cauchy numbers of the first kind. In addition, we give the asymptotic expansion of certain sums involving 2-associated Stirling numbers of the second kind by Darboux’s method.

Key concepts: Stirling numbers of the first kind, Stirling numbers of the second kind, Stirling number, Bernoulli number, Mathematics, Harmonic number, Stirling engine, Bell polynomials

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