code: def test_airybiprime():
      z = Symbol("z", real=False)
      t = Symbol("t", negative=True)
      p = Symbol("p", positive=True)
  
      assert isinstance(airybiprime(z), airybiprime)
  
      assert airybiprime(0) == 3 ** Rational(1, 6) / gamma(
          Rational(1, 3)
      )
      assert airybiprime(oo) is oo
      assert airybiprime(-oo) == 0
  
      assert diff(airybiprime(z), z) == z * airybi(z)
  
      assert series(airybiprime(z), z, 0, 3) == (
          3 ** Rational(1, 6) / gamma(Rational(1, 3))
          + 3 ** Rational(5, 6) * z**2 / (6 * gamma(Rational(2, 3)))
          + O(z**3)
      )
  
      assert airybiprime(z).rewrite(hyper) == (
          3 ** Rational(5, 6)
          * z**2
          * hyper((), (Rational(5, 3),), z**3 / 9)
          / (6 * gamma(Rational(2, 3)))
          + 3 ** Rational(1, 6)
          * hyper((), (Rational(1, 3),), z**3 / 9)
          / gamma(Rational(1, 3))
      )
  
      assert isinstance(airybiprime(z).rewrite(besselj), airybiprime)
      assert airyai(t).rewrite(besselj) == (
          sqrt(-t)
          * (
              besselj(Rational(-1, 3), 2 * (-t) ** Rational(3, 2) / 3)
              + besselj(Rational(1, 3), 2 * (-t) ** Rational(3, 2) / 3)
          )
          / 3
      )
      assert airybiprime(z).rewrite(besseli) == (
          sqrt(3)
          * (
              z**2
              * besseli(Rational(2, 3), 2 * z ** Rational(3, 2) / 3)
              / (z ** Rational(3, 2)) ** Rational(2, 3)
              + (z ** Rational(3, 2)) ** Rational(2, 3)
              * besseli(Rational(-2, 3), 2 * z ** Rational(3, 2) / 3)
          )
          / 3
      )
      assert airybiprime(p).rewrite(besseli) == (
          sqrt(3)
          * p
          * (
              besseli(Rational(-2, 3), 2 * p ** Rational(3, 2) / 3)
              + besseli(Rational(2, 3), 2 * p ** Rational(3, 2) / 3)
          )
          / 3
      )
  
      assert expand_func(
          airybiprime(2 * (3 * z**5) ** Rational(1, 3))
      ) == (
          sqrt(3)
          * (z ** Rational(5, 3) / (z**5) ** Rational(1, 3) - 1)
          * airyaiprime(2 * 3 ** Rational(1, 3) * z ** Rational(5, 3))
          / 2
          + (z ** Rational(5, 3) / (z**5) ** Rational(1, 3) + 1)
          * airybiprime(2 * 3 ** Rational(1, 3) * z ** Rational(5, 3))
          / 2
      )
  
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 31 for calling a global function with example usage: test_airybiprime() without return types