Uniform asymptotic approximations for the Lam\'{e} and Mathieu functions and their respective eigenvalues with a large parameter
Classical Analysis and ODEs
2015-07-31 v3
Abstract
By application of the theory for second-order linear differential equations with two turning points developed in \cite{Olver1975}, uniform asymptotic approximations are obtained for the Lam\'{e} and Mathieu functions with a large real parameter. The approximations are expressed in terms of parabolic cylinder functions, and are uniformly valid in their respective real open intervals. In all cases explicit bounds are supplied for the error terms associated with the approximations. Approximations are also obtained for their respective eigenvalues.
Cite
@article{arxiv.1507.04981,
title = {Uniform asymptotic approximations for the Lam\'{e} and Mathieu functions and their respective eigenvalues with a large parameter},
author = {Karen Ogilvie and Adri B. Olde Daalhuis},
journal= {arXiv preprint arXiv:1507.04981},
year = {2015}
}
Comments
Removed due to paper merger