 ##  [Poisson Summation Formula](/poisson-summation-formula) 

  ##  [Poisson Summation Formula](https://puremath.quantumdictionary.io/poisson-summation-formula-0) 

  
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- Mathematics &amp; Logic -

**Pure Mathematics Dictionary**

 
Definition

The equality that relates the sum of a function sampled on a lattice in Euclidean space to the sum of its Fourier transform sampled on the dual lattice; commonly expressed for functions on R^n as sum_{m in Z^n} f(m) = sum_{k in Z^n} 36f(k), making a precise bridge between discrete sums and harmonic analysis.