On a version of quaternionic function theory related to mathieu functions

The angular and radial Mathieu functions, or elliptic-cylinder functions, are solutions of the two ordinary differential equations of the second order with variable coefficients and were originally proposed by È. Mathieu in 1868 for finding the modes in en elliptic membrane. Since then, they have found numerous and important applications to the problems in physics and engineering science thus generating a vast research literature about them. It's appeared recently that there exists a theory of functions with quaternionic values and of two real variables which is determined by a Cauchy-Riemann-type operator with quaternionic, variable coefficients and which is intimately related to the Mathieu equations. In the work, it is explained all the above and some basic facts of the arising quaternionic function theory.