Important for elliptical shapes and periodic potentials, the Wolfram Language achieves a new level of implementation for Mathieu-related functions, supporting arbitrary-precision evaluation for all complex values of parameters.

Mathieu Functions and Derivatives

MathieuS  ▪  MathieuC  ▪  MathieuSPrime  ▪  MathieuCPrime

Characteristic Values and Exponents

MathieuCharacteristicA  ▪  MathieuCharacteristicB  ▪  MathieuCharacteristicExponent