code: def test_recursive():
      from sympy.core.symbol import symbols
  
      a, b, c = symbols("a b c", positive=True)
      r = exp(-((x - a) ** 2)) * exp(-((x - b) ** 2))
      e = integrate(r, (x, 0, oo), meijerg=True)
      assert simplify(e.expand()) == (
          sqrt(2)
          * sqrt(pi)
          * (
              (erf(sqrt(2) * (a + b) / 2) + 1)
              * exp(-(a**2) / 2 + a * b - b**2 / 2)
          )
          / 4
      )
      e = integrate(
          exp(-((x - a) ** 2)) * exp(-((x - b) ** 2)) * exp(c * x),
          (x, 0, oo),
          meijerg=True,
      )
      assert simplify(e) == (
          sqrt(2)
          * sqrt(pi)
          * (erf(sqrt(2) * (2 * a + 2 * b + c) / 4) + 1)
          * exp(-(a**2) - b**2 + (2 * a + 2 * b + c) ** 2 / 8)
          / 4
      )
      assert simplify(
          integrate(
              exp(-((x - a - b - c) ** 2)), (x, 0, oo), meijerg=True
          )
      ) == sqrt(pi) / 2 * (1 + erf(a + b + c))
      assert simplify(
          integrate(
              exp(-((x + a + b + c) ** 2)), (x, 0, oo), meijerg=True
          )
      ) == sqrt(pi) / 2 * (1 - erf(a + b + c))
  
imports: from sympy.core.function import expand_func
  from sympy.core.numbers import I, Rational, oo, pi
  from sympy.core.singleton import S
  from sympy.core.sorting import default_sort_key
  from sympy.functions.elementary.complexes import Abs, arg, re, unpolarify
  from sympy.functions.elementary.exponential import exp, exp_polar, log
  from sympy.functions.elementary.hyperbolic import cosh, acosh
  from sympy.functions.elementary.miscellaneous import sqrt
  from sympy.functions.elementary.piecewise import Piecewise, piecewise_fold
  from sympy.functions.elementary.trigonometric import cos, sin, sinc, asin
  from sympy.functions.special.error_functions import erf, erfc
  from sympy.functions.special.gamma_functions import gamma, polygamma
  from sympy.functions.special.hyper import hyper, meijerg
  from sympy.integrals.integrals import Integral, integrate
  from sympy.simplify.hyperexpand import hyperexpand
  from sympy.simplify.simplify import simplify
  from sympy.integrals.meijerint import _rewrite_single, _rewrite1, meijerint_indefinite, _inflate_g, _create_lookup_table, meijerint_definite, meijerint_inversion
  from sympy.testing.pytest import slow
  from sympy.core.random import verify_numerically, random_complex_number
  from sympy.abc import x, y, a, b, c, d, s, t, z
label_desc: Use image node_id 6 for calling a global function with example usage: test_recursive() without return types