A note on inverse central factorial series

Abstract

The purpose of this brief note is to draw attention to a type of inverse factorial series which, so far as the writer can judge, has not been intensively studied. The central difference formulae of interpolation and the corresponding infinite series in central factorial polynomials have in the past received much attention, and so also has the ordinary inverse factorial serieswhich from the time of Stirling (Methodus Differentialis, 1730) has been known to be of value in transforming slowly convergent series into series of more rapid convergence.