Surprising Sinc Sums and Integrals.

The article attempts to demonstrate that a variety of trigonometric sums have unexpected closed forms by relating them to cognate integrals. It calculates the sinc sums through the equation sinc(x) := sin (x)/x when x not equal to 0 and sinc(0) := 1. It shows that the theorems for integrals proven in a certain equation imply analogues for sums. It provides the application when sums and integrals agree based on Boas and Pollard using Fourier analysis. It provides the applications to sinc sums and integrals.