On the Equivalence of Fourier Expansion and Poisson Summation Formula for the Series Approximation of the Exponential Function

摘要

In this short note we show the equivalence of Fourier expansion and Poissonsummation approaches for the series approximation of the exponential function$\exp ({-{t^2}/4})$. The application of the Poisson summation formula is shownto reduce to that of the Fourier expansion method.