# Clebsch Gordan coefficients

I'm trying to compute various sums which contain some CG coefficients, where the sum runs over the indexes m1,m2,m corresponding to each of the three angular momenta j1,j2,j. The thing is that when I try to evaluate such a sum, Mathematica shows some errors and then it throws the message "General::stop: Further output of ClebschGordan::phy will be suppressed during this calculation."

sum[j1_, j2_, j_] := Sum[ClebschGordan[{j1, m1}, {j2, m2}, {j, m}], {m1, -j1, j1,
1}, {m2, -j2, j2, 1}, {m, -j, j, 1}];
N[sum[6, 2, 4]]
Do[Print[ClebschGordan[{6, m1}, {2, m2}, {4, m}]], {m1, -6, 6, 1}, {m2, -2, 2, 1}, {m, -4, 4, 1}]


I understand that for some values of {j1,m2},{j2,m2},{j,m} the CG coefficients are zero, but why does Mathematica throw error messages instead of just ignoring the term and keep going forward with the evaluation? Does the output error message mean that after a certain coefficient, Mathematica just simply stops evaluating terms, and my result will be incorrect?

• It is only a message , not an error. See documentation of ThreeJSymbol/ possible issues – Ulrich Neumann Apr 15 at 7:50
• @RobertPoenaru You can also suppress this very particular warning message with Off[ClebschGordan::phy] right from the start; this might even accelerate the evaluation since message handling is quite costly in Mathematica since the FrontEnd has to be involved each time a message is thrown. – Henrik Schumacher Apr 15 at 8:33