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      Explicit formulas for computing Bernoulli numbers of the second kind and Stirling numbers of the first kind

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          Abstract

          In the paper, by establishing a new and explicit formula for computing the \(n\)-th derivative of the reciprocal of the logarithmic function, the author presents new and explicit formulas for calculating Bernoulli numbers of the second kind and Stirling numbers of the first kind. As consequences of these formulas, a recursion for Stirling numbers of the first kind and a new representation of the reciprocal of the factorial \(n!\) are derived. Finally, the author finds several identities and integral representations relating to Stirling numbers of the first kind.

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          Author and article information

          Journal
          29 January 2013
          Article
          10.2298/FIL1402319O
          1301.6845
          2870d9d1-ec89-4e20-ad09-31f883097217

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

          Custom metadata
          Primary 11B68, Secondary 05A10, 11B65, 11B73, 11B83, 26A24, 33B10
          Filomat 28 (2014), no. 2, 319--327
          9 pages
          math.CO math.CA math.NT

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