diff --git a/tests/unit_tests/test_math.py b/tests/unit_tests/test_math.py
index 6825f6b93..a63561854 100644
--- a/tests/unit_tests/test_math.py
+++ b/tests/unit_tests/test_math.py
@@ -57,9 +57,30 @@ def test_evaluate_legendre():
     test_vals = np.array([openmc.capi.math.evaluate_legendre(test_coeffs, x)
                           for x in test_xs])
 
+    # When turn on the flag 2, evaluate_legendre should be the same as
+    # np.polynomial.legendre.legval().
+    test_coeffs = [(2. * l + 1.) / 10 for l in range(max_order + 1)]
+    ref_vals_1 = np.polynomial.legendre.legval(test_xs, test_coeffs)
+
+    test_vals_1 = np.array([openmc.capi.math.evaluate_legendre(test_coeffs, x,
+                            2)for x in test_xs])
+
+    assert np.allclose(ref_vals, test_vals)
+    assert np.allclose(ref_vals_1, test_vals_1)
+
+
+def test_calc_norm_pn():
+    max_order = 10
+    zmin = -10
+    zmax = 10
+
+    ref_vals = np.divide(2 * np.arange(max_order + 1) + 1, (zmax-zmin))
+
+    test_vals = openmc.capi.math.calc_norm_pn(max_order, zmin, zmax)
+
     assert np.allclose(ref_vals, test_vals)
 
-
+    
 def test_calc_rn():
     max_order = 10
     test_ns = np.array([i for i in range(0, max_order + 1)])
@@ -137,6 +158,32 @@ def test_calc_zn():
     assert np.allclose(ref_vals, test_vals)
 
 
+def test_calc_zn_rad():
+    n = 10
+    rho = 0.5
+    phi = 0.5
+
+    # Reference solution from running the Fortran implementation
+    ref_vals = np.array([
+        1.00000000e+00, -5.00000000e-01, -1.25000000e-01,
+        4.37500000e-01, -2.89062500e-01,-8.98437500e-02])
+
+    test_vals = openmc.capi.math.calc_zn_rad(n, rho)
+
+    assert np.allclose(ref_vals, test_vals)
+
+
+def test_calc_norm_zn_rad():
+    max_order = 10
+    rho = 0.5
+
+    ref_vals = np.divide(np.arange(0, max_order + 1, 2) + 1, np.pi * rho * rho)
+
+    test_vals = openmc.capi.math.calc_norm_zn_rad(max_order, rho)
+
+    assert np.allclose(ref_vals, test_vals)
+
+
 def test_rotate_angle():
     uvw0 = np.array([1., 0., 0.])
     phi = 0.