Poisson Summation and an Infinite Expansion for tan(ax)

We discuss the Poisson summation formula and apply it twice. We use the fact that the Fourier transform performed twice is composition with -x toward with the Fourier Transform of a Tent Function (Fejer Kernel) to derive a symmetric infinite series for tan(ax) when a is not an integer.

#mikethemathematician, #mikedabkowski, #profdabkowski

[robertgreene]

It does not affect the result but at some point there is an x written for what should be an alpha(. Otherwise very nice. This is an exercise in Stein and Shakarchi