def test_hermite():
assert hermite(0, x) == 1
assert hermite(1, x) == 2 * x
assert hermite(2, x) == 4 * x**2 - 2
assert hermite(3, x) == 8 * x**3 - 12 * x
assert hermite(4, x) == 16 * x**4 - 48 * x**2 + 12
assert hermite(6, x) == 64 * x**6 - 480 * x**4 + 720 * x**2 - 120
assert hermite(n, x) == hermite(n, x)
assert hermite(n, -x) == (-1)**n * hermite(n, x)
assert hermite(-n, x) == hermite(-n, x)
assert hermite(n, 0) == 2**n * sqrt(pi) / gamma((1 - n) / 2)
assert hermite(n, oo) == oo
assert conjugate(hermite(n, x)) == hermite(n, conjugate(x))
assert diff(hermite(n, x), x) == 2 * n * hermite(n - 1, x)
assert diff(hermite(n, x), n) == Derivative(hermite(n, x), n)
def test_hermite():
assert hermite(0, x) == 1
assert hermite(1, x) == 2*x
assert hermite(2, x) == 4*x**2 - 2
assert hermite(3, x) == 8*x**3 - 12*x
assert hermite(4, x) == 16*x**4 - 48*x**2 + 12
assert hermite(6, x) == 64*x**6 - 480*x**4 + 720*x**2 - 120
assert hermite(n, x) == hermite(n, x)
assert hermite(n, -x) == (-1)**n*hermite(n, x)
assert hermite(-n, x) == hermite(-n, x)
assert hermite(n, 0) == 2**n*sqrt(pi)/gamma((1 - n)/2)
assert hermite(n, oo) == oo
pytest.raises(ValueError, lambda: hermite(-1, x))
assert conjugate(hermite(n, x)) == hermite(n, conjugate(x))
assert diff(hermite(n, x), x) == 2*n*hermite(n - 1, x)
assert diff(hermite(n, x), n) == Derivative(hermite(n, x), n)