def clebsch_gordan(j_1, j_2, j_3, m_1, m_2, m_3):
 res = ((((-1) ** sympify(((j_1 - j_2) + m_3))) * sqrt(((2 * j_3) + 1))) * wigner_3j(j_1, j_2, j_3, m_1, m_2, (- m_3)))
 return res

def clebsch_gordan ( j_1 , j_2 , j_3 , m_1 , m_2 , m_3 ) : res = ( ( ( ( - 1 ) ** sympify ( ( ( j_1 - j_2 ) + m_3 ) ) ) * sqrt ( ( ( 2 * j_3 ) + 1 ) ) ) * wigner_3j ( j_1 , j_2 , j_3 , m_1 , m_2 , ( - m_3 ) ) ) return res
calculates the clebsch-gordan coefficient langle j_1 m_1 ; j_2 m_2 | j_3 m_3 rangle .