Properties and applications of the reciprocal logarithm numbers
The author investigates the sequence of rational numbers \((A_k)_{k\geq 0}\), which he calls the ``reciprocal logarithm numbers'' defined by the series expansion \(1/\ln(1+z) = \sum_{k=0}^\infty A_k z^{k-1}\). He derives several properties of these numbers such as recursions, integral representations and identities. More specifically, he points out the relationship of the \(A_k\)'s to Stirling numbers of the first kind and to Euler's constant. A similar approach is then presented for the series expansion of \(1/\arctan x\).
scientific article; zbMATH DE number 5700597