code: def test_sph_kn(self):
      kn = np.empty((2, 3))
      x = 0.2
  
      kn[0][0] = spherical_kn(0, x)
      kn[0][1] = spherical_kn(1, x)
      kn[0][2] = spherical_kn(2, x)
      kn[1][0] = spherical_kn(0, x, derivative=True)
      kn[1][1] = spherical_kn(1, x, derivative=True)
      kn[1][2] = spherical_kn(2, x, derivative=True)
  
      kn0 = -kn[0][1]
      kn1 = -kn[0][0] - 2.0 / 0.2 * kn[0][1]
      kn2 = -kn[0][1] - 3.0 / 0.2 * kn[0][2]
      assert_array_almost_equal(
          kn[0],
          [
              6.4302962978445670140,
              38.581777787067402086,
              585.15696310385559829,
          ],
          12,
      )
      assert_array_almost_equal(kn[1], [kn0, kn1, kn2], 9)
  
imports: import numpy
  from numpy.testing import assert_almost_equal, assert_allclose, assert_array_almost_equal, suppress_warnings
  import pytest
  from numpy import sin, cos, sinh, cosh, exp, inf, nan, r_, pi
  from scipy.special import spherical_jn, spherical_yn, spherical_in, spherical_kn
  from scipy.integrate import quad
label_desc: Use image node_id 4 for calling the TestSphericalOld obj's underlying member method code with example usage: obj.test_sph_kn() without return types