A note on some asymptotic properties of the logarithmic series distribution

SUMMARYFormulae are given to calculate S(x, R) = ∞Σr−R+1 x7/r9 the remainder term in the logarithmic series, which are valid for high values of R and values of x close to unity. These are of value when dealing with extreme values of the parameters appearing in the logarithmic series distribution such as have arisen in C. B. William's recent study of the possible distribution of the number per species for all the insects in the world. Bounds are given for the errors involved when making the recommended approximations. The calculation of the median of the distribution is also discussed.