https://doi.org/10.1051/epjconf/201716201064
Mathieu functions and its useful approximation for elliptical waveguides
Faculty of Engineering Multimedia University Cyberjaya Malaysia
* Corresponding author: shamini.pillay@mmu.edu.my
Published online: 22 November 2017
The standard form of the Mathieu differential equation is 
where a and q are real parameters and q > 0. In this paper we obtain closed formula for the generic term of expansions of modified Mathieu functions in terms of Bessel and modified Bessel functions in the following cases: 
Let ξ0 = ξ0, where i can take the values 1 and 2 corresponding to the first and the second boundary. These approximations also provide alternative methods for numerical evaluation of Mathieu functions.
© The Authors, published by EDP Sciences, 2017
This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (http://creativecommons.org/licenses/by/4.0/).
