code: def test_fresnel_series():
      assert fresnelc(z).series(
          z, n=15
      ) == z - pi**2 * z**5 / 40 + pi**4 * z**9 / 3456 - pi**6 * z**13 / 599040 + O(
          z**15
      )
  
      # issues 6510, 10102
      fs = (
          S.Half
          - sin(pi * z**2 / 2) / (pi**2 * z**3)
          + (-1 / (pi * z) + 3 / (pi**3 * z**5))
          * cos(pi * z**2 / 2)
      )
      fc = (
          S.Half
          - cos(pi * z**2 / 2) / (pi**2 * z**3)
          + (1 / (pi * z) - 3 / (pi**3 * z**5))
          * sin(pi * z**2 / 2)
      )
      assert fresnels(z).series(z, oo) == fs + O(z ** (-6), (z, oo))
      assert fresnelc(z).series(z, oo) == fc + O(z ** (-6), (z, oo))
      assert (
          (fresnels(z).series(z, -oo) + fs.subs(z, -z))
          .expand()
          .is_Order
      )
      assert (
          (fresnelc(z).series(z, -oo) + fc.subs(z, -z))
          .expand()
          .is_Order
      )
      assert (
          (fresnels(1 / z).series(z) - fs.subs(z, 1 / z))
          .expand()
          .is_Order
      )
      assert (
          (fresnelc(1 / z).series(z) - fc.subs(z, 1 / z))
          .expand()
          .is_Order
      )
      assert (
          ((2 * fresnels(3 * z)).series(z, oo) - 2 * fs.subs(z, 3 * z))
          .expand()
          .is_Order
      )
      assert (
          ((3 * fresnelc(2 * z)).series(z, oo) - 3 * fc.subs(z, 2 * z))
          .expand()
          .is_Order
      )
  
imports: from sympy.core.function import diff, expand, expand_func
  from sympy.core import EulerGamma
  from sympy.core.numbers import E, Float, I, Rational, nan, oo, pi
  from sympy.core.singleton import S
  from sympy.core.symbol import Symbol, symbols
  from sympy.functions.elementary.complexes import conjugate, im, polar_lift, re
  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, sinc
  from sympy.functions.special.error_functions import Chi, Ci, E1, Ei, Li, Shi, Si, erf, erf2, erf2inv, erfc, erfcinv, erfi, erfinv, expint, fresnelc, fresnels, li
  from sympy.functions.special.gamma_functions import gamma, uppergamma
  from sympy.functions.special.hyper import hyper, meijerg
  from sympy.integrals.integrals import Integral, integrate
  from sympy.series.gruntz import gruntz
  from sympy.series.limits import limit
  from sympy.series.order import O
  from sympy.core.expr import unchanged
  from sympy.core.function import ArgumentIndexError
  from sympy.functions.special.error_functions import _erfs, _eis
  from sympy.testing.pytest import raises
label_desc: Use image node_id 28 for calling a global function with example usage: test_fresnel_series() without return types