code: def test_factorial2_rewrite():
      n = Symbol("n", integer=True)
      assert factorial2(n).rewrite(gamma) == 2 ** (n / 2) * Piecewise(
          (1, Eq(Mod(n, 2), 0)), (sqrt(2) / sqrt(pi), Eq(Mod(n, 2), 1))
      ) * gamma(n / 2 + 1)
      assert factorial2(2 * n).rewrite(gamma) == 2**n * gamma(n + 1)
      assert factorial2(2 * n + 1).rewrite(gamma) == sqrt(2) * 2 ** (
          n + S.Half
      ) * gamma(n + Rational(3, 2)) / sqrt(pi)
  
imports: from sympy.concrete.products import Product
  from sympy.core.function import expand_func
  from sympy.core.mod import Mod
  from sympy.core.mul import Mul
  from sympy.core import EulerGamma
  from sympy.core.numbers import Float, I, Rational, nan, oo, pi, zoo
  from sympy.core.relational import Eq
  from sympy.core.singleton import S
  from sympy.core.symbol import Dummy, Symbol, symbols
  from sympy.functions.combinatorial.factorials import ff, rf, binomial, factorial, factorial2
  from sympy.functions.elementary.miscellaneous import sqrt
  from sympy.functions.elementary.piecewise import Piecewise
  from sympy.functions.special.gamma_functions import gamma, polygamma
  from sympy.polys.polytools import Poly
  from sympy.series.order import O
  from sympy.simplify.simplify import simplify
  from sympy.core.expr import unchanged
  from sympy.core.function import ArgumentIndexError
  from sympy.functions.combinatorial.factorials import subfactorial
  from sympy.functions.special.gamma_functions import uppergamma
  from sympy.testing.pytest import XFAIL, raises, slow
label_desc: Use image node_id 11 for calling a global function with example usage: test_factorial2_rewrite() without return types