code: def test_betainc_regularized():
      a, b, x1, x2 = symbols("a b x1 x2")
  
      assert unchanged(betainc_regularized, a, b, x1, x2)
      assert unchanged(betainc_regularized, a, b, 0, x1)
  
      assert betainc_regularized(3, 5, 0, -1).is_real == True
      assert betainc_regularized(3, 5, 0, x2).is_real is None
      assert conjugate(
          betainc_regularized(3 * I, 1, 2 + I, 1 + 2 * I)
      ) == betainc_regularized(-3 * I, 1, 2 - I, 1 - 2 * I)
  
      assert betainc_regularized(a, b, 0, 1).rewrite(Integral) == 1
      assert betainc_regularized(1, 2, x1, x2).rewrite(
          hyper
      ) == 2 * x2 * hyper((1, -1), (2,), x2) - 2 * x1 * hyper(
          (1, -1), (2,), x1
      )
  
      assert betainc_regularized(4, 1, 5, 5).evalf() == 0
  
file_path: sympy/sympy/functions/special/tests/test_beta_functions.py
imports: from sympy.core.function import diff, expand_func
  from sympy.core.numbers import I, Rational, pi
  from sympy.core.singleton import S
  from sympy.core.symbol import Dummy, symbols
  from sympy.functions.combinatorial.numbers import catalan
  from sympy.functions.elementary.complexes import conjugate
  from sympy.functions.elementary.miscellaneous import sqrt
  from sympy.functions.special.beta_functions import beta, betainc, betainc_regularized
  from sympy.functions.special.gamma_functions import gamma, polygamma
  from sympy.functions.special.hyper import hyper
  from sympy.integrals.integrals import Integral
  from sympy.core.function import ArgumentIndexError
  from sympy.core.expr import unchanged
  from sympy.testing.pytest import raises
label_desc: Use image node_id 3 for calling a global function with example usage: test_betainc_regularized() without return types