and for each respective and , and hence also all pre-factors in eventually become indistinguishable from . Therefore the functions and their respective Fourier transforms converge to the same function and this limit function is a series of infinite equidistant Gaussian spikes, each spike being multiplied by the same pre-factor of one, i.e., the Dirac comb for unit period:
: and

Since , we obtain in this limit the result to be demonstrated:
: The corresponding result for period can be found by exploiting