Sums of products of Cauchy numbers |
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Authors: | Feng-Zhen Zhao |
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Affiliation: | Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, China |
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Abstract: | In this paper, we consider a kind of sums involving Cauchy numbers, which have not been studied in the literature. By means of the method of coefficients, we give some properties of the sums. We further derive some recurrence relations and establish a series of identities involving the sums, Stirling numbers, generalized Bernoulli numbers, generalized Euler numbers, Lah numbers, and harmonic numbers. In particular, we generalize some relations between two kinds of Cauchy numbers and some identities for Cauchy numbers and Stirling numbers. |
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Keywords: | Cauchy numbers Stirling numbers Harmonic numbers Lah numbers Generating functions Recurrence relations Asymptotic expansion |
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