query: Expression for the Fourier transform of $f(x) = \frac{1}{1 +\|x\|^2}$
positive_passages.docid: 24653
positive_passages.text: Integral in $n-$dimensional euclidean space
negative_passages.docid: 37546
negative_passages.text: Fourier Series for $|\cos(x)|$
negative_passages.docid: 51837
negative_passages.text: Show that $\int_{0}^{\pi} xf(\sin(x))\text{d}x = \frac{\pi}{2}\int_{0}^{\pi}f(\sin(x))\text{d}x$
negative_passages.docid: 100401
negative_passages.text: Evaluate $\int \frac{1}{(x^2+1)^2}dx$
negative_passages.docid: 115992
negative_passages.text: Integrating $\frac{\log(1+x)}{1+x^2}$
negative_passages.docid: 118715
negative_passages.text: Inverse Laplace transform of $\frac{1}{s\sinh{c\sqrt{s}}}$
negative_passages.docid: 124335
negative_passages.text: An identity for Fourier transform of measure
negative_passages.docid: 57686
negative_passages.text: Finding $ \int^1_0 \frac{\ln(1+x)}{x}dx$
negative_passages.docid: 119447
negative_passages.text: Scaling property of  Fourier series and Fourier Transform
negative_passages.docid: 13671
negative_passages.text: Fourier Transform of Various Tempered Distributions
negative_passages.docid: 20025
negative_passages.text: Fourier transform of $\exp(-t^2)$ using contour integration.
negative_passages.docid: 47572
negative_passages.text: Evaluate $ \sum_{n=1}^{\infty} \frac{\sin \ n}{ n } $ using the fourier series
negative_passages.docid: 144811
negative_passages.text: Calculate $\int_0^{2\pi} \frac{1}{2+\sin(x)} \ dx$
negative_passages.docid: 100606
negative_passages.text: Fourier transform of a radial function is radial
negative_passages.docid: 124164
negative_passages.text: ($n$-dimensional) Inverse Fourier transform of $\frac{1}{\| \mathbf{\omega} \|^{2\alpha}}$
negative_passages.docid: 67606
negative_passages.text: Derive Fourier transform of sinc function
negative_passages.docid: 114195
negative_passages.text: Evaluating $\int_0^\infty \frac{\log (1+x)}{1+x^2}dx$