A Note on the Asymptotic Expansion of a Ratio of Gamma Functions

Abstract

Many problems in mathematical analysis require a knowledge of the asymptotic behaviour of Γ(z + α)/Γ(z + β) for large values of |z|, where α and β are bounded quantities. Tricomi and Erdélyi in (1), gave the asymptotic expansionwhere the are the generalised Bernoulli polynomials, see (2), defined byIn this note, we show that if, instead of considering z to be the large variable, we consider a related large variable, (1) can be improved from a computational viewpoint.