It's a rigorous result if you define it as an analytic continuation of the Riemann zeta function defined in the normal way. It doesn't take much to prove, but t

It's a rigorous result if you define it as an analytic continuation of the Riemann zeta function defined in the normal way. It doesn't take much to prove, but the way it's used in physics it's not always immediately clear that interpreting infinite and divergent sums as analytic continuations of finite sums is justified. Yet it seems to work...