query: Taking inverse Fourier transform of $\frac{\sin^2(\pi s)}{(\pi s)^2}$
positive_passages.docid: 156531
positive_passages.text: Evaluating the integral $\int_{-\infty}^\infty \frac{\sin^2(x)}{x^2}e^{i t x} dx$
negative_passages.docid: 148940
negative_passages.text: $\sum_{n=1}^\infty\frac1{n^6}=\frac{\pi^6}{945}$ by Fourier series of $x^2$
negative_passages.docid: 151127
negative_passages.text: Confirm that $\int_{0}^{\infty}t^{-1}\sin t dt=\pi/2$
negative_passages.docid: 15242
negative_passages.text: What's the correct way to shift zero frequency to the center of a Fourier Transform?
negative_passages.docid: 20025
negative_passages.text: Fourier transform of $\exp(-t^2)$ using contour integration.
negative_passages.docid: 87242
negative_passages.text: Ways to prove $ \int_0^\pi dx \frac{\sin^2(n x)}{\sin^2 x} = n\pi$
negative_passages.docid: 137551
negative_passages.text: integral $\int_0^\pi \frac{\cos(2t)}{a^2\sin^2(t)+b^2\cos^2(t)}dt$
negative_passages.docid: 62450
negative_passages.text: Computing $ \int_0^{2\pi} \frac{1}{a^2\cos^2 t+b^2 \sin^2 t} dt \;; a,b>0$.
negative_passages.docid: 136996
negative_passages.text: Fourier transform of function composition
negative_passages.docid: 113045
negative_passages.text: How do I find the inverse of $f(x) = \frac{x}{x^2 + 1}$
negative_passages.docid: 93825
negative_passages.text: Fourier transform of power function $t^\alpha$
negative_passages.docid: 9477
negative_passages.text: Dft to evaluate Fourier coefficients
negative_passages.docid: 146067
negative_passages.text: Creating intuition about Laplace & Fourier transforms
negative_passages.docid: 130736
negative_passages.text: Integrating $\int^0_\pi \frac{x \sin x}{1+\cos^2 x}$
negative_passages.docid: 97418
negative_passages.text: Fourier Transform of Derivative
negative_passages.docid: 82027
negative_passages.text: How to derive compositions of trigonometric and inverse trigonometric functions?
negative_passages.docid: 18335
negative_passages.text: Fourier transform of a radial function