code: def test_meijerg_eval():
      from sympy.functions.elementary.exponential import exp_polar
      from sympy.functions.special.bessel import besseli
      from sympy.abc import l
  
      a = randcplx()
      arg = x * exp_polar(k * pi * I)
      expr1 = pi * meijerg(
          [[], [(a + 1) / 2]],
          [[a / 2], [-a / 2, (a + 1) / 2]],
          arg**2 / 4,
      )
      expr2 = besseli(a, arg)
  
      # Test that the two expressions agree for all arguments.
      for x_ in [0.5, 1.5]:
          for k_ in [0.0, 0.1, 0.3, 0.5, 0.8, 1, 5.751, 15.3]:
              assert abs((expr1 - expr2).n(subs={x: x_, k: k_})) < 1e-10
              assert (
                  abs((expr1 - expr2).n(subs={x: x_, k: -k_})) < 1e-10
              )
  
      # Test continuity independently
      eps = 1e-13
      expr2 = expr1.subs(k, l)
      for x_ in [0.5, 1.5]:
          for k_ in [
              0.5,
              Rational(1, 3),
              0.25,
              0.75,
              Rational(2, 3),
              1.0,
              1.5,
          ]:
              assert (
                  abs(
                      (expr1 - expr2).n(
                          subs={x: x_, k: k_ + eps, l: k_ - eps}
                      )
                  )
                  < 1e-10
              )
              assert (
                  abs(
                      (expr1 - expr2).n(
                          subs={x: x_, k: -k_ + eps, l: -k_ - eps}
                      )
                  )
                  < 1e-10
              )
  
      expr = (
          meijerg(
              ((0.5,), ()), ((0.5, 0, 0.5), ()), exp_polar(-I * pi) / 4
          )
          + meijerg(
              ((0.5,), ()), ((0.5, 0, 0.5), ()), exp_polar(I * pi) / 4
          )
      ) / (2 * sqrt(pi))
      assert (expr - pi / exp(1)).n(chop=True) == 0
  
imports: from sympy.core.containers import Tuple
  from sympy.core.function import Derivative
  from sympy.core.numbers import I, Rational, oo, pi
  from sympy.core.singleton import S
  from sympy.core.symbol import symbols
  from sympy.functions.elementary.exponential import exp, log
  from sympy.functions.elementary.miscellaneous import sqrt
  from sympy.functions.elementary.trigonometric import cos
  from sympy.functions.special.gamma_functions import gamma
  from sympy.functions.special.hyper import appellf1, hyper, meijerg
  from sympy.series.order import O
  from sympy.abc import x, z, k
  from sympy.series.limits import limit
  from sympy.testing.pytest import raises, slow
  from sympy.core.random import random_complex_number, verify_numerically, test_derivative_numerically
label_desc: Use image node_id 12 for calling a global function with example usage: test_meijerg_eval() without return types