New summation formulas for multivariate infinite series by using sampling theorems

Abstract

The aim of this paper is to show how sampling theory can play an important rol in summing up infinite series in several variables. This will be demonstrated by deriving severa summation formulas for doubly infinite series that are believed to be new. One of the interesting features of this works i that although the formulas appear to be cojmplicated, their proofs are rather eqasy and straightforward when sampling theorems are employed. The summation formulas are derived by using theorems on both uniform and non-unifrom sampling.