from typing_extensions import Self

from sympy.core.function import Function, UndefinedFunction
from sympy.core.mul import Mul

class MathieuBase(Function):
    unbranched = ...

class mathieus(MathieuBase):
    def fdiff(self, argindex=...) -> type[UndefinedFunction]: ...
    @classmethod
    def eval(cls, a, q, z) -> type[UndefinedFunction] | Mul | None: ...

class mathieuc(MathieuBase):
    def fdiff(self, argindex=...) -> type[UndefinedFunction]: ...
    @classmethod
    def eval(cls, a, q, z) -> type[UndefinedFunction] | Self | None: ...

class mathieusprime(MathieuBase):
    def fdiff(self, argindex=...): ...
    @classmethod
    def eval(cls, a, q, z) -> Self | None: ...

class mathieucprime(MathieuBase):
    def fdiff(self, argindex=...): ...
    @classmethod
    def eval(cls, a, q, z) -> Mul | None: ...