XVII.—On the Asymptotic Expansion of the Characteristic Numbers of the Mathieu Equation
- 1 January 1930
- journal article
- conference paper
- Published by Cambridge University Press (CUP) in Proceedings of the Royal Society of Edinburgh
- Vol. 49, 210-223
- https://doi.org/10.1017/s0370164600026407
Abstract
An asymptotic formula has recently been given for the characteristic numbers of the Mathieu equation From tabular values, it will be seen that the formula provides good numerical approximations to the characteristic numbers of integral order; but as pointed out by Ince, it provides better approximations to the characteristic numbers of order (m + ½), where m is a positive integer or zero. In this paper we shall first attempt to find out why this should be so, and then go on to show that the formula is probably an asymptotic expansion, in the Poincaré sense, for any characteristic number. A new asymptotic formula is then found for the difference between two characteristic numbers.Keywords
This publication has 1 reference indexed in Scilit:
- A Note on Certain Approximate Solutions of Linear Differential Equations of the Second Order, with an Application to the Mathieu EquationProceedings of the London Mathematical Society, 1928