A method for the determination of converging factors, applied to the asymptotic expansions for the parabolic cylinder functions
- 1 April 1952
- journal article
- research article
- Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society
- Vol. 48 (2), 243-254
- https://doi.org/10.1017/s0305004100027602
Abstract
1. The method of converging factors, for hastening the convergence of slowly convergentseries and improving the accuracy of asymptotic expansions, was introduced by J. R. Airey and is well known to computers (see Airey(1) and Rosser(2)). The principle is as follows. It is required to compute a quantity which is expressed as an infinite seriesThe series may be either convergent or asymptotic and divergent.Keywords
This publication has 3 references indexed in Scilit:
- Transformations to speed the convergence of seriesJournal of Research of the National Bureau of Standards, 1951
- LII.The “converging factor” in asymptotic series and the calculation of Bessel, laguerre and other functionsJournal of Computers in Education, 1937
- Recherches sur quelques séries semi-convergentesAnnales Scientifiques de lʼÉcole Normale Supérieure, 1886