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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.
MathieuS ▪ MathieuC ▪ MathieuSPrime ▪ MathieuCPrime
MathieuCharacteristicA ▪ MathieuCharacteristicB ▪ MathieuCharacteristicExponent