Explicit formulas for computing Bernoulli numbers of the second kind and Stirling numbers of the first kind
Combinatorics
2014-05-06 v1 Classical Analysis and ODEs
Number Theory
Abstract
In the paper, by establishing a new and explicit formula for computing the -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 are derived. Finally, the author finds several identities and integral representations relating to Stirling numbers of the first kind.
Keywords
Cite
@article{arxiv.1301.6845,
title = {Explicit formulas for computing Bernoulli numbers of the second kind and Stirling numbers of the first kind},
author = {Feng Qi},
journal= {arXiv preprint arXiv:1301.6845},
year = {2014}
}
Comments
9 pages