# Questions tagged [poisson-summation-formula]

For questions dealing with the Poisson Summation Formula

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I am trying to evaluate the following expression for $\lambda \in \mathbb{R}$ : $$f(\lambda)=\sum_{n=1}^{+\infty}e^{-i\lambda n}$$ My idea is to introduce an epsilon prescription, so I choose $\... 0answers 99 views ### Minkowski's Theorem by Harmonic Analysis I am trying to properly write a proof of Minkowski's theorem in a self-contained way and understandable by (good) undergraduates. Theorem (Minkowski) Let$L$be a lattice of$\mathbb{R}^n$and ... 0answers 51 views ### Formal Poisson summation formula I want to prove the following equality: $$\lim_{a\to -\infty,b\to \infty}\sum_{n=a}^b \frac {\sin \pi (c+n)}{\pi (c+n)}=1,\text{ for any }c\in \mathbb R.$$ All solutions I found directs me to an ... 0answers 98 views ### Poisson summation formula and Fourier series Let's consider the function$F(x,y)$defined by: $$F(x,y)= \sum_{n=1}^{\infty} f(nx) e^{-2 i \pi ny}$$ with$f(x)$decreasing exponentially at infinity,$f(x)=0$and$\int_{-\infty}^{\infty} f(|t|)dt=...
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I am making a model in Matlab that calculates the winning probability of darts player A against darts player B with help of a paper (see bottom line). I have been able to implement the calculation of ...
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### Simplifying Summation That Occurs In Poisson Counting Process

The question of how to compute the probability of an even or odd value occurring in the Poisson counting process has been answered on here in several places, but there's a step in the solution that I ...