code: def test_hermite_poly():
      raises(ValueError, lambda: hermite_poly(-1, x))
  
      assert hermite_poly(1, x, polys=True) == Poly(2 * x)
  
      assert hermite_poly(0, x) == 1
      assert hermite_poly(1, x) == 2 * x
      assert hermite_poly(2, x) == 4 * x**2 - 2
      assert hermite_poly(3, x) == 8 * x**3 - 12 * x
      assert hermite_poly(4, x) == 16 * x**4 - 48 * x**2 + 12
      assert hermite_poly(5, x) == 32 * x**5 - 160 * x**3 + 120 * x
      assert (
          hermite_poly(6, x)
          == 64 * x**6 - 480 * x**4 + 720 * x**2 - 120
      )
  
      assert hermite_poly(1).dummy_eq(2 * x)
      assert hermite_poly(1, polys=True) == Poly(2 * x)
  
file_path: sympy/sympy/polys/tests/test_orthopolys.py
imports: from sympy.core.numbers import Rational
  from sympy.core.singleton import S
  from sympy.core.symbol import symbols
  from sympy.polys.polytools import Poly
  from sympy.testing.pytest import raises
  from sympy.polys.orthopolys import jacobi_poly, gegenbauer_poly, chebyshevt_poly, chebyshevu_poly, hermite_poly, hermite_prob_poly, legendre_poly, laguerre_poly, spherical_bessel_fn
  from sympy.abc import x, a, b
label_desc: Use image node_id 5 for calling a global function with example usage: test_hermite_poly() without return types