The expression ClebschGordan[{2, 0}, {4, 0}, {2, 0}]
yields the correct result of Sqrt[2/7]
.
However the expression ClebschGordan[{2, 0}, {l2, 0}, {2, 0}]/. l2 -> 4
yields Indeterminate
. Indeed, ClebschGordan[{2, 0}, {l2, 0}, {2, 0}]
evaluates to an algebraic expression numerator/((-4 + l2) (2 - l2)!)
where numerator/.l2 -> 4
evaluates to Sqrt[2/7]
. This is indeed indeterminate.
Interestingly, the expression ClebschGordan[{l2, 0}, {2, 0}, {2, 0}] /. l2 -> 4
gives the correct result, and ClebschGordan[{l2, 0}, {2, 0}, {2, 0}]
leads to a different algebraic expression that has the same values for 0<=l2<4
and the correct value for l2->4
.
This would appear to be a minor bug, as it violates the simplest symmetry of the Clebsch-Gordan coefficients.
ClebschGordan[{j, m}, {j1, m1}, {j2, m2}] /. {j -> 2, m -> 0, j1 -> 4, m1 -> 0, j2 -> 2, m2 -> 0}
returnsSqrt[2/7]
. The substitution can also be done stepwise and the correct result is still obtained. Odd behavior indeed. $\endgroup$