1108.0300 (Wei He)

Combinatorial approach to Mathieu and Lamé equations    [PDF]

Wei He

Based on some recent progress on a relation between four dimensional super Yang-Mills gauge theory and quantum integrable system, we give a combinatorial method to derive the asymptotic expansions for eigenvalues of the Mathieu and Lam\'{e} equations. The WKB method is also used to extend the expansions in one asymptotic region to other asymptotic regions.

View original: http://arxiv.org/abs/1108.0300