The heavenly gates? Not so fast, calculus sinner! The Math Pope has caught you committing the cardinal sin of mathematical analysis - illegally swapping the order of summation and integration. That innocent-looking equation is actually a serious no-no without checking convergence conditions first.
For the uninitiated: this operation is only valid under specific conditions (uniform convergence, anyone?). Mathematicians have nightmares about this! Swap these operations without proper justification and you'll face eternal damnation in the infinite series of mathematical hell where all your proofs have "left as an exercise to the reader" at the critical steps.