Examples of Heun and Mathieu functions as solutions of wave equations in   curved spaces
  We give examples where the Heun function exists in general relativity. It turns out that while a wave equation written in the background of certain metric yields Mathieu functions as its solutions in four space-time dimensions, the trivial generalization to five dimensions results in the double confluent Heun function. We reduce this solution to the Mathieu function with some transformations. 
T. Birkandan, M. Hortacsu