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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.

### Author and article information

###### Journal
29 January 2013
###### Article
10.2298/FIL1402319O
1301.6845