code: def _noncentral_chi_pdf(t, df, nc):
      res = mpmath.besseli(df / 2 - 1, mpmath.sqrt(nc * t))
      res *= (
          mpmath.exp(-(t + nc) / 2) * (t / nc) ** (df / 4 - 1 / 2) / 2
      )
      return res
  
imports: import itertools
  import numpy
  from numpy.testing import assert_equal, assert_allclose
  import pytest
  import scipy.special
  from scipy.special._testutils import MissingModule, check_version, FuncData
  from scipy.special._mptestutils import Arg, IntArg, get_args, mpf2float, assert_mpmath_equal
label_desc: Use image node_id 5 for calling a global function with example usage: _noncentral_chi_pdf(t, df, nc) and returns: res