query: Fourier transform of $e^{-\frac{1}{2}x^2}$
positive_passages.docid: 23059
positive_passages.text: How to calculate the Fourier transform of a Gaussian function?
negative_passages.docid: 35982
negative_passages.text: A function and its Fourier transform cannot both be compactly supported
negative_passages.docid: 123934
negative_passages.text: a Fourier transform (sinc)
negative_passages.docid: 77721
negative_passages.text: Is it possible to compute $\int_1^{+ \infty} \frac{dx}{x^2(1+e^x)}$?
negative_passages.docid: 81057
negative_passages.text: Evaluation of $\int_{\frac{1}{e}}^{\tan x}\frac{t}{1+t^2}dt+\int_{\frac{1}{e}}^{\cot x}\frac{1}{t(1+t^2)}dt$
negative_passages.docid: 135967
negative_passages.text: What is the odd Fourier extension of $\sin x \cos(2x)$?
negative_passages.docid: 12698
negative_passages.text: Orthonormal basis for $\mathcal{L}^2([0,1])$
negative_passages.docid: 10675
negative_passages.text: Proving that $\frac{1}{2\pi}\int_{0}^{2\pi}|f(re^{it})|^2dt=\sum_{n=0}^{\infty}|a_n|^2r^{2n}$
negative_passages.docid: 18335
negative_passages.text: Fourier transform of a radial function
negative_passages.docid: 32312
negative_passages.text: Evaluating the integral $\int \frac{x^2+x}{(e^x+x+1)^2}dx$
negative_passages.docid: 5167
negative_passages.text: Finding the limit that involves Fourier coefficients,
negative_passages.docid: 44737
negative_passages.text: $ \int_{-\infty}^{\infty} x^4 e^{-ax^2} dx$
negative_passages.docid: 143585
negative_passages.text: Solve the integral $\frac 1 {\sqrt {2 \pi t}}\int_{-\infty}^{\infty} x^2 e^{-\frac {x^2} {2t}}dx$
negative_passages.docid: 13671
negative_passages.text: Fourier Transform of Various Tempered Distributions
negative_passages.docid: 65732
negative_passages.text: Inverse Fourier transform
negative_passages.docid: 9944
negative_passages.text: Fourier series identity
negative_passages.docid: 116520
negative_passages.text: formula for the $n$th derivative of $e^{-1/x^2}$