Closed form solution for acoustic wave equation between two parallel plates using Euler–Maclaurin sum formula

The Euler–Maclaurin sum formula is applied to the infinite series of images in the Green function for acoustic wave propagation between two perfectly reflecting parallel plates. The major part of the series is represented with an integral representation by the formula. The formula also provides a reminder. An approximate closed form solution is obtained for the Green function, including both an exact major part and an approximate remainder. It is applied to the transient response for an exponentially decaying point acoustic source located between the plates. For a specific numerical example, the approximate closed form solution is compared to infinite series summation.