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Gaussian Integral

Gaussian Integral

72K viewsFeb 10, 2022

FacebookExtra-math

Fourier Integral & 3D Gaussian Wave

Fourier Integral & 3D Gaussian Wave

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FacebookMath is Visual

In this exercise, we prove the normalization condition (1.48) for the univariate Gaussian. To do this consider, the integral I=∫-∞^∞ (-(1)/(2 σ^2) x^2) d x which we can evaluate by first writing its square in the form I^2=∫-∞^∞ ∫-∞^∞ (-(1)/(2 σ^2) x^2-(1)/(2 σ^2) y^2) d x d y Now make the transformation from Cartesian coordinates (x, y) to polar coordinates (r, θ) and then substitute u=r^2. Show that, by performing the integrals over θand u, and then taking the square root of both sides, we obt

In this exercise, we prove the normalization condition (1.48) for …

Step-by-step solution for the Gaussian Integral

Step-by-step solution for the Gaussian Integral

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Generalities on the Gaussian Integrals

Generalities on the Gaussian Integrals

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YouTubeTimur Obolenskiy

Solving all these integrals, and beyond (Generalized Gaussian Integral)

Solving all these integrals, and beyond (Generalized Gaussian Int…

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Exploring the Gaussian Integral

Exploring the Gaussian Integral

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Applications of Taylor polynomials: an integral and special relativity

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