remove f3prime function

ichor_core/ichor/core/multipoles/hexadecapole.py

@@ -371,27 +371,6 @@ def f3(
     return dipole_alpha * oct_prime + dipole_prime * oct_beta_gamma_chi
 
 
-# TODO: remove this function after hexadecupole works
-def f3prime(gamma, beta, alpha, dipole, octupole, displacement_vector):
-
-    dipole_term = dipole[gamma]
-
-    displacement_alpha = displacement_vector[alpha]
-    displacement_beta = displacement_vector[beta]
-    displacement_gamma = displacement_vector[gamma]
-
-    return (
-        0.5
-        * dipole_term
-        * (
-            4 * displacement_beta * displacement_alpha**2
-            - displacement_beta**3
-            - displacement_beta * displacement_gamma**2
-        )
-        + displacement_gamma * octupole[beta, alpha, alpha]
-    )
-
-
 def f4(alpha, beta, gamma, chi, quadrupole, displacement_vector):
 
     theta_alpha_beta = quadrupole[alpha, beta]
@@ -601,10 +580,7 @@ def G(alpha, beta, gamma, chi, dipole, quadrupole, octupole, displacement_vector
         )
         term2 = 10.5 * (
             f3(beta, gamma, alpha, alpha, dipole, octupole, displacement_vector)
-            + f3(
-                gamma, beta, alpha, alpha, dipole, octupole, displacement_vector
-            )  # TODO: remove this comment after hexadecupole works
-            # f3prime(gamma, beta, alpha, dipole, octupole, displacement_vector)
+            + f3(gamma, beta, alpha, alpha, dipole, octupole, displacement_vector)
         )
         term3 = 3 * (
             f3(beta, gamma, beta, beta, dipole, octupole, displacement_vector)