code: def test_trigamma():
      assert trigamma(nan) == nan
  
      assert trigamma(oo) == 0
  
      assert trigamma(1) == pi**2 / 6
      assert trigamma(2) == pi**2 / 6 - 1
      assert trigamma(3) == pi**2 / 6 - Rational(5, 4)
  
      assert trigamma(x, evaluate=False).rewrite(zeta) == zeta(2, x)
      assert trigamma(x, evaluate=False).rewrite(harmonic) == trigamma(
          x
      ).rewrite(polygamma).rewrite(harmonic)
  
      assert trigamma(x, evaluate=False).fdiff() == polygamma(2, x)
  
      assert trigamma(x, evaluate=False).is_real is None
  
      assert trigamma(x, evaluate=False).is_positive is None
  
      assert trigamma(x, evaluate=False).is_negative is None
  
      assert trigamma(x, evaluate=False).rewrite(
          polygamma
      ) == polygamma(1, x)
  
imports: from sympy.core.function import expand_func, Subs
  from sympy.core import EulerGamma
  from sympy.core.numbers import I, Rational, nan, oo, pi, zoo
  from sympy.core.singleton import S
  from sympy.core.symbol import Dummy, Symbol
  from sympy.functions.combinatorial.factorials import factorial
  from sympy.functions.combinatorial.numbers import harmonic
  from sympy.functions.elementary.complexes import Abs, conjugate, im, re
  from sympy.functions.elementary.exponential import exp, exp_polar, log
  from sympy.functions.elementary.hyperbolic import tanh
  from sympy.functions.elementary.miscellaneous import sqrt
  from sympy.functions.elementary.trigonometric import cos, sin, atan
  from sympy.functions.special.error_functions import Ei, erf, erfc
  from sympy.functions.special.gamma_functions import digamma, gamma, loggamma, lowergamma, multigamma, polygamma, trigamma, uppergamma
  from sympy.functions.special.zeta_functions import zeta
  from sympy.series.order import O
  from sympy.core.expr import unchanged
  from sympy.core.function import ArgumentIndexError
  from sympy.testing.pytest import raises
  from sympy.core.random import test_derivative_numerically, random_complex_number, verify_numerically
label_desc: Use image node_id 11 for calling a global function with example usage: test_trigamma() without return types