code: def test_slow_expand():
      def check(eq, ans):
          return tn(eq, ans) and eq == ans
  
      rn = randcplx(a=1, b=0, d=0, c=2)
  
      for besselx in [besselj, bessely, besseli, besselk]:
          ri = (
              S(2 * randint(-11, 10) + 1) / 2
          )  # half integer in [-21/2, 21/2]
          assert tn(besselsimp(besselx(ri, z)), besselx(ri, z))
  
      assert check(
          expand_func(besseli(rn, x)),
          besseli(rn - 2, x) - 2 * (rn - 1) * besseli(rn - 1, x) / x,
      )
      assert check(
          expand_func(besseli(-rn, x)),
          besseli(-rn + 2, x) + 2 * (-rn + 1) * besseli(-rn + 1, x) / x,
      )
  
      assert check(
          expand_func(besselj(rn, x)),
          -besselj(rn - 2, x) + 2 * (rn - 1) * besselj(rn - 1, x) / x,
      )
      assert check(
          expand_func(besselj(-rn, x)),
          -besselj(-rn + 2, x)
          + 2 * (-rn + 1) * besselj(-rn + 1, x) / x,
      )
  
      assert check(
          expand_func(besselk(rn, x)),
          besselk(rn - 2, x) + 2 * (rn - 1) * besselk(rn - 1, x) / x,
      )
      assert check(
          expand_func(besselk(-rn, x)),
          besselk(-rn + 2, x) - 2 * (-rn + 1) * besselk(-rn + 1, x) / x,
      )
  
      assert check(
          expand_func(bessely(rn, x)),
          -bessely(rn - 2, x) + 2 * (rn - 1) * bessely(rn - 1, x) / x,
      )
      assert check(
          expand_func(bessely(-rn, x)),
          -bessely(-rn + 2, x)
          + 2 * (-rn + 1) * bessely(-rn + 1, x) / x,
      )
  
imports: from itertools import product
  from sympy.concrete.summations import Sum
  from sympy.core.function import diff, expand_func
  from sympy.core.numbers import I, Rational, oo, pi
  from sympy.core.singleton import S
  from sympy.core.symbol import Symbol, symbols
  from sympy.functions.elementary.complexes import conjugate, polar_lift
  from sympy.functions.elementary.exponential import exp, exp_polar, log
  from sympy.functions.elementary.hyperbolic import cosh, sinh
  from sympy.functions.elementary.miscellaneous import sqrt
  from sympy.functions.elementary.trigonometric import cos, sin
  from sympy.functions.special.bessel import besseli, besselj, besselk, bessely, hankel1, hankel2, hn1, hn2, jn, jn_zeros, yn
  from sympy.functions.special.gamma_functions import gamma, uppergamma
  from sympy.functions.special.hyper import hyper
  from sympy.integrals.integrals import Integral
  from sympy.series.order import O
  from sympy.series.series import series
  from sympy.functions.special.bessel import airyai, airybi, airyaiprime, airybiprime, marcumq
  from sympy.core.random import random_complex_number, verify_numerically, test_derivative_numerically, _randint
  from sympy.simplify import besselsimp
  from sympy.testing.pytest import raises, slow
  from sympy.abc import z, n, k, x
label_desc: Use image node_id 14 for calling a global function with example usage: test_slow_expand() and returns: unknown