where "f" is a cutoff function with appropriate properties. The cutoff function must be normalized to ; this is a different normalization from the one used in differential equations. The cutoff function should have enough bounded derivatives to smooth out the wrinkles in the series, and it should decay to 0 faster than the series grows. For convenience, one may require that "f" is smooth, bounded, and compactly supported. One can then prove that this smoothed sum is asymptotic to , where "C" is a constant that depends on "f". The constant term of the asymptotic expansion does not depend on "f": it is necessarily the same value given by analytic continuation, .