code: def test_besselj_series():
      assert besselj(0, x).series(
          x
      ) == 1 - x**2 / 4 + x**4 / 64 + O(x**6)
      assert besselj(0, x ** (1.1)).series(
          x
      ) == 1 + x**4.4 / 64 - x**2.2 / 4 + O(x**6)
      assert besselj(0, x**2 + x).series(
          x
      ) == 1 - x**2 / 4 - x**3 / 2 - 15 * x**4 / 64 + x**5 / 16 + O(
          x**6
      )
      assert besselj(0, sqrt(x) + x).series(
          x, n=4
      ) == 1 - x / 4 - 15 * x**2 / 64 + 215 * x**3 / 2304 - x ** Rational(
          3, 2
      ) / 2 + x ** Rational(
          5, 2
      ) / 16 + 23 * x ** Rational(
          7, 2
      ) / 384 + O(
          x**4
      )
      assert besselj(0, x / (1 - x)).series(
          x
      ) == 1 - x**2 / 4 - x**3 / 2 - 47 * x**4 / 64 - 15 * x**5 / 16 + O(
          x**6
      )
      assert besselj(0, log(1 + x)).series(
          x
      ) == 1 - x**2 / 4 + x**3 / 4 - 41 * x**4 / 192 + 17 * x**5 / 96 + O(
          x**6
      )
      assert besselj(1, sin(x)).series(
          x
      ) == x / 2 - 7 * x**3 / 48 + 73 * x**5 / 1920 + O(x**6)
      assert besselj(1, 2 * sqrt(x)).series(x) == sqrt(
          x
      ) - x ** Rational(3, 2) / 2 + x ** Rational(
          5, 2
      ) / 12 - x ** Rational(
          7, 2
      ) / 144 + x ** Rational(
          9, 2
      ) / 2880 - x ** Rational(
          11, 2
      ) / 86400 + O(
          x**6
      )
      assert besselj(-2, sin(x)).series(x, n=4) == besselj(
          2, sin(x)
      ).series(x, n=4)
  
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 7 for calling a global function with example usage: test_besselj_series() without return types