code: def test_branching():
      assert besselj(polar_lift(k), x) == besselj(k, x)
      assert besseli(polar_lift(k), x) == besseli(k, x)
  
      n = Symbol("n", integer=True)
      assert besselj(n, exp_polar(2 * pi * I) * x) == besselj(n, x)
      assert besselj(n, polar_lift(x)) == besselj(n, x)
      assert besseli(n, exp_polar(2 * pi * I) * x) == besseli(n, x)
      assert besseli(n, polar_lift(x)) == besseli(n, x)
  
      def tn(func, s):
          from sympy.core.random import uniform
  
          c = uniform(1, 5)
          expr = func(s, c * exp_polar(I * pi)) - func(
              s, c * exp_polar(-I * pi)
          )
          eps = 1e-15
          expr2 = func(s + eps, -c + eps * I) - func(
              s + eps, -c - eps * I
          )
          return abs(expr.n() - expr2.n()).n() < 1e-10
  
      nu = Symbol("nu")
      assert besselj(nu, exp_polar(2 * pi * I) * x) == exp(
          2 * pi * I * nu
      ) * besselj(nu, x)
      assert besseli(nu, exp_polar(2 * pi * I) * x) == exp(
          2 * pi * I * nu
      ) * besseli(nu, x)
      assert tn(besselj, 2)
      assert tn(besselj, pi)
      assert tn(besselj, I)
      assert tn(besseli, 2)
      assert tn(besseli, pi)
      assert tn(besseli, I)
  
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 26 for calling a global function with example usage: test_branching() and returns: unknown