Confluence of singularities of differential equation: a Lie algebra contraction approach

Abstract

We investigate here the confluence of singularities of Mathieu differential equation by means of the Lie algebra contraction of the Lie algebra of the motion group M(2) on the Heisenberg Lie algebra H(3). A similar approach for the Lamé equation in terms of the Lie algebra contraction of $S{O}_0(2,1)$ on the Lie algebra of the motion group M(2) is outlined.