I came across the Mathieu functions when solving a PDE with Mathematica.
My solution was of the form $f=C_1Mat_C + C_2 Mat_S$
AFAIK those are the non periodical Mathieu functions, which are different from the periodic ones (Cos-elliptic and Sin-elliptic).
What i was looking for is a reference with an extensive treatment of both periodic and non periodic Mathieu functions, covering their properties and with some applicative examples (i come from the physics community).
Thank you!