A Note on the Asymptotic Expansion of a Ratio of Gamma Functions
- 1 June 1966
- journal article
- research article
- Published by Cambridge University Press (CUP) in Proceedings of the Edinburgh Mathematical Society
- Vol. 15 (1), 43-45
- https://doi.org/10.1017/s0013091500013171
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.Keywords
This publication has 3 references indexed in Scilit:
- The asymptotic expansion of a ratio of gamma functionsPacific Journal of Mathematics, 1951
- An Approximation to the Quotient of Gamma FunctionThe American Mathematical Monthly, 1949
- Vorlesungen über DifferenzenrechnungPublished by Springer Science and Business Media LLC ,1924