Poprawione definicje współczynników Clebscha-Gordana oraz symboli 3j, 6j i 9j

(*"corrected" Clebsch-Gordan coefficients are defined*)myClebschGordan[j1_,j2_,j3_,m1_,m2_,m3_]:=If[(Abs[m1]≤j1)&&(Abs[m2]≤j2)&&(Abs[m3]≤j3)&&(m1+m2==m3)&&(j1+j2≥j3)&&(Abs[j1-j2]≤j3),ClebschGordan[{j1,m1},{j2,m2},{j3,m3}],0];

(*"corrected" 3j-symbol *)myThreeJSymbol[j1_,j2_,j3_,m1_,m2_,m3_]:=(-1)^(j1-j2-m3)/Sqrt[2*j3+1]*myClebschGordan[j1,j2,j3,m1,m2,-m3]

(* "corrected" 6j-symbol *)
mySixJSymbol[j1_,j2_,j12_,j3_,j_,j23_]:=If[(Abs[j1-j2]≤j12)&&(Abs[j2-j3]≤j23)&&(Abs[j12-j3]≤j)&&(Abs[j1-j23]≤j)&&(j1+j2≥j12)&&(j2+j3≥j23)&&(j12+j3≥j)&&(j1+j23≥j),SixJSymbol[{j1,j2,j12},{j3,j,j23}],0];

(* "hand-made" definition of 9j-coefficient *)
NineJSymbol[j11_,j12_,j13_,j21_,j22_,j23_,j31_,j32_,j33_]:=Sum[(-1)^(2*k)*(2*k+1) mySixJSymbol[j11,j21,j31,j32,j33,k] mySixJSymbol[j12,j22,j32,j21,k,j23] mySixJSymbol[j13,j23,j33,k,j11,j12],{k,Abs[j21-j32],j21+j32,1}];

N[myClebschGordan[2,1,2,-2,1,-1],12]

N[myClebschGordan[1,1,2,0,0,0],12]

N[myThreeJSymbol[2,1,2,-2,1,1],12]

N[mySixJSymbol[1/2,1/2,1,1/2,1/2,1],12]

N[NineJSymbol[4,1,4,
                             3,1/2,7/2,
                              6,3/2,9/2],12]

N[mySixJSymbol[1,1,1,1/2,3/2,1/2],12]

mySixJSymbol[1,1,1,1/2,3/2,1/2]

10.954451150103322^2