English

Eigenvalue Problems for Lam\'e's Differential Equation

Classical Analysis and ODEs 2018-12-13 v2

Abstract

The Floquet eigenvalue problem and a generalized form of the Wangerin eigenvalue problem for Lam\'e's differential equation are discussed. Results include comparison theorems for eigenvalues and analytic continuation, zeros and limiting cases of (generalized) Lam\'e-Wangerin eigenfunctions. Algebraic Lam\'e functions and Lam\'e polynomials appear as special cases of Lam\'e-Wangerin functions.

Keywords

Cite

@article{arxiv.1808.04877,
  title  = {Eigenvalue Problems for Lam\'e's Differential Equation},
  author = {Hans Volkmer},
  journal= {arXiv preprint arXiv:1808.04877},
  year   = {2018}
}