query: Showing that the Gaussian function is a fixed point of the Fourier transformation using Complex Analysis
positive_passages.docid: 20025
positive_passages.text: Fourier transform of $\exp(-t^2)$ using contour integration.
negative_passages.docid: 16722
negative_passages.text: Proving Gaussian Integers are countable
negative_passages.docid: 43551
negative_passages.text: Difficulty in understanding a part in a proof from Stein and Shakarchi Fourier Analysis book.
negative_passages.docid: 158971
negative_passages.text: Computing the Fourier series of $f(\theta)=(\pi-\theta)^2/4$ for $0\leq\theta\leq{2\pi}$
negative_passages.docid: 105494
negative_passages.text: Gaussian-like integral : $\int_0^{\infty} e^{-x^2} \cos( a x) \ \mathrm{d}x$
negative_passages.docid: 152339
negative_passages.text: Complex-valued Fourier integral: $ \int_{ - \infty }^{ + \infty } {\frac{{\cos (ax)}}{{{x^2} + 1}}{e^{ - ibx}}\,\mathrm dx} $
negative_passages.docid: 43440
negative_passages.text: Complex Analysis: Showing analytic function is zero
negative_passages.docid: 13671
negative_passages.text: Fourier Transform of Various Tempered Distributions
negative_passages.docid: 136635
negative_passages.text: Proving that the Fourier Basis is complete for C(R/$2*\pi$ , C) with $L^2$ norm
negative_passages.docid: 107070
negative_passages.text: Fourier transform standard practice for physics
negative_passages.docid: 119447
negative_passages.text: Scaling property of  Fourier series and Fourier Transform
negative_passages.docid: 81863
negative_passages.text: Gaussian integral with imaginary coefficients and Wick rotation
negative_passages.docid: 69614
negative_passages.text: a generalization of normal distribution to the complex case: complex integral over the real line
negative_passages.docid: 37546
negative_passages.text: Fourier Series for $|\cos(x)|$
negative_passages.docid: 12239
negative_passages.text: Holomorphic function with a fixed point
negative_passages.docid: 100606
negative_passages.text: Fourier transform of a radial function is radial
negative_passages.docid: 16049
negative_passages.text: Fourier transform of $\int_{-\infty}^{t}f(t)\, dt$