Explicit expressions for higher order convolutions of Cauchy numbers
Jos\'e A. Adell, Alberto Lekuona
TL;DR
This paper derives explicit formulas for higher order convolutions of Cauchy numbers, expressing them through integrals and Stirling numbers, enhancing understanding of their combinatorial properties.
Contribution
It introduces new explicit integral and Stirling number-based formulas for higher order convolutions of Cauchy numbers, advancing their analytical study.
Findings
Explicit integral expressions for convolutions.
Formulas involving Stirling numbers of both kinds.
Enhanced tools for analyzing Cauchy number convolutions.
Abstract
We give explicit expressions for higher order convolutions of Cauchy numbers, either as one single integral or in terms of the Stirling numbers of the first and second kinds.
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Taxonomy
TopicsAdvanced Mathematical Identities · Advanced Combinatorial Mathematics · Mathematical functions and polynomials