Integrate[(Sum[BesselJ[n, r], {n, 0, 10}])^2*r, {r, 0, [Infinity]}] Result is -9.20481 The integral of square of Sum of BesselJ function from 0 to 10 order, but give a negative result. This shouldn't be, because it is a real function and after square it is all greater or equal zero and r is also positive or zero. The result should be positive. Anything could be wrong with Mathematica?
Integrate[(Sum[BesselJ[n, r], {n, 0, 10}])^2*r, {r, 0, \[Infinity]}, GenerateConditions -> True]
reports that the integral does not converge. I guess with the default setting for GenerateConditions, it is not so careful.
GenerateConditions
