Question

How do I prove that $\left(\frac{1}{10^5} \sum_{n=-\infty}^{\infty} e^{\frac{-n^2}{10^{10}}}\right)^2 \approx \pi? $

score 110 · Answer 1 · 2026-04-09 11:46:38

110

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How do I prove that $\left(\frac{1}{10^5} \sum_{n=-\infty}^{\infty} e^{\frac{-n^2}{10^{10}}}\right)^2 \approx \pi? $

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List Question

How do I prove that $\left(\frac{1}{10^5} \sum_{n=-\infty}^{\infty} e^{\frac{-n^2}{10^{10}}}\right)^2 \approx \pi? $

Conections between Parseval's Identities

Period and Fourier series

Derivative of the Dirac delta function. The Fourier transform of this function is the a-th derivative of the Dirac delta function. How to interprete?

Extremely rigorous (research level) treatment of the laplace transform

L_1 norm of spherical harmonics

Fourier transform of $\frac{1}{|x|}$ on $\mathbb{T}^{n}$

A Littlewood-Paley question

FFT Basic Question

Rate of convergence of fourier series for non periodic functions

double doubt working with fourier inverse theorem and a calculation of a sup

Is the convolution of a tempered distribution and a Schwartz function also a function?

Asymptotics of a multi-dimensional Fourier series

Do there exist mathematical transforms other than the Fourier Transform for which there exists some sort of a fast convolution theorem?

Do mollifiers exist in dimensions higher than 1?

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