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

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