from typing import Any

from sympy.concrete.summations import Sum
from sympy.core.function import Function, UndefinedFunction
from sympy.core.mul import Mul
from sympy.core.relational import Equality, Ne, Relational

_x = ...

class OrthogonalPolynomial(Function): ...

class jacobi(OrthogonalPolynomial):
    @classmethod
    def eval(cls, n, a, b, x) -> type[UndefinedFunction] | Any | None: ...
    def fdiff(self, argindex=...) -> Equality | Relational | Ne | Sum: ...

def jacobi_normalized(n, a, b, x): ...

class gegenbauer(OrthogonalPolynomial):
    @classmethod
    def eval(cls, n, a, x) -> type[UndefinedFunction] | None: ...
    def fdiff(self, argindex=...) -> Equality | Relational | Ne | Sum: ...

class chebyshevt(OrthogonalPolynomial):
    _ortho_poly = ...
    @classmethod
    def eval(cls, n, x) -> type[UndefinedFunction] | None: ...
    def fdiff(self, argindex=...): ...

class chebyshevu(OrthogonalPolynomial):
    _ortho_poly = ...
    @classmethod
    def eval(cls, n, x) -> type[UndefinedFunction] | None: ...
    def fdiff(self, argindex=...): ...

class chebyshevt_root(Function):
    @classmethod
    def eval(cls, n, k) -> type[UndefinedFunction]: ...

class chebyshevu_root(Function):
    @classmethod
    def eval(cls, n, k) -> type[UndefinedFunction]: ...

class legendre(OrthogonalPolynomial):
    _ortho_poly = ...
    @classmethod
    def eval(cls, n, x) -> type[UndefinedFunction] | None: ...
    def fdiff(self, argindex=...): ...

class assoc_legendre(Function):
    @classmethod
    def eval(cls, n, m, x) -> type[UndefinedFunction] | None: ...
    def fdiff(self, argindex=...): ...

class hermite(OrthogonalPolynomial):
    _ortho_poly = ...
    @classmethod
    def eval(cls, n, x) -> None: ...
    def fdiff(self, argindex=...): ...

class hermite_prob(OrthogonalPolynomial):
    _ortho_poly = ...
    @classmethod
    def eval(cls, n, x) -> None: ...
    def fdiff(self, argindex=...): ...

class laguerre(OrthogonalPolynomial):
    _ortho_poly = ...
    @classmethod
    def eval(cls, n, x) -> None: ...
    def fdiff(self, argindex=...) -> Mul: ...

class assoc_laguerre(OrthogonalPolynomial):
    @classmethod
    def eval(cls, n, alpha, x) -> type[UndefinedFunction] | Any | None: ...
    def fdiff(self, argindex=...) -> Equality | Relational | Ne | Sum | Mul: ...