Question

Demonstration of an identity between a simple and a double integral of a Gaussian-Lorentzian product

score 59 · Answer 1 · 2023-11-07 14:12:44

59

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Demonstration of an identity between a simple and a double integral of a Gaussian-Lorentzian product

Published on 07 Nov 2023 - 14:12

score 46 · Answer 2 · 2023-11-09 01:21:04

46

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Extending Laplace transform to multivariate cases?

Published on 09 Nov 2023 - 1:21

score 38 · Answer 3 · 2023-11-09 08:41:00

38

Views

If $f \neq 0$, do we have $\int_{ x_i \geq 0} f(x) e^{-\sum_{i=1}^n c_i x_i^2} d^nx \neq 0$ for some $c \in (0,\infty)^n$?

Published on 09 Nov 2023 - 8:41

score 84 · Answer 4 · 2023-11-21 15:10:55

84

Views

a special type of Gaussian Integral (reciperocal Quadratic functions with Gaussian Integral)

Published on 21 Nov 2023 - 15:10

score 39 · Answer 5 · 2023-11-21 15:40:34

39

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Is the function $\int_0^{1} e^{-t H}e^{-2x^2}dt$ in $L^2$ with respect to the gaussian measure?

Published on 21 Nov 2023 - 15:40

score 254 · Answer 6 · 2023-11-22 09:06:50

254

Views

Integral over a small set is small and dimension independent

Published on 22 Nov 2023 - 9:06

score 52 · Answer 7 · 2023-11-27 11:43:03

52

Views

A partition function problem under conserved total momentum, involving Gaussian integration under a delta constraint

Published on 27 Nov 2023 - 11:43

score 214 · Answer 8 · 2023-12-09 22:41:32

214

Views

What is the integral $\int_{-\infty}^{+\infty} x^{-2} e^{-x^2}\,dx$?

Published on 09 Dec 2023 - 22:41

score 51 · Answer 9 · 2023-12-12 22:41:58

51

Views

Generalization of Laplace's integral

Published on 12 Dec 2023 - 22:41

score 84 · Answer 10 · 2023-12-15 11:31:38

84

Views

Computing Gaussian-Weighted Integrals for Small Lengthscales

Published on 15 Dec 2023 - 11:31

score 67 · Answer 11 · 2023-12-24 00:42:06

67

Views

Seeking Probability Function Invariant under Normal Gaussian Convolution

Published on 24 Dec 2023 - 0:42

score 229 · Answer 12 · 2026-03-25 16:01:37

229

Views

Log-convexity of a function defined by an integral (Normal Mills ratio)

Published on 25 Mar 2026 - 16:01

score 22 · Answer 13 · 2023-12-28 17:30:51

22

Views

Given a multilinear polynomial $g$, and an odd function $f$ show that $\int f(x_i) \exp(-\| x \|^2) g(x-y) d x =0, \forall y,i$ where $g(x)=c$)

Published on 28 Dec 2023 - 17:30

score 107 · Answer 14 · 2026-03-25 17:32:44

107

Views

Integrating a product of Gaussian kernels

Published on 25 Mar 2026 - 17:32

score 95 · Answer 15 · 2024-01-12 12:30:11

95

Views

What does $\int_{B_r} h$ mean? Problem 3-41 in "Calculus on Manifolds" by Michael Spivak. $\int_{-\infty}^{\infty}e^{-x^2}dx=\sqrt{\pi}$.

Published on 12 Jan 2024 - 12:30

List Question

Demonstration of an identity between a simple and a double integral of a Gaussian-Lorentzian product

Extending Laplace transform to multivariate cases?

If $f \neq 0$, do we have $\int_{ x_i \geq 0} f(x) e^{-\sum_{i=1}^n c_i x_i^2} d^nx \neq 0$ for some $c \in (0,\infty)^n$?

a special type of Gaussian Integral (reciperocal Quadratic functions with Gaussian Integral)

Is the function $\int_0^{1} e^{-t H}e^{-2x^2}dt$ in $L^2$ with respect to the gaussian measure?

Integral over a small set is small and dimension independent

A partition function problem under conserved total momentum, involving Gaussian integration under a delta constraint

What is the integral $\int_{-\infty}^{+\infty} x^{-2} e^{-x^2}\,dx$?

Generalization of Laplace's integral

Computing Gaussian-Weighted Integrals for Small Lengthscales

Seeking Probability Function Invariant under Normal Gaussian Convolution

Log-convexity of a function defined by an integral (Normal Mills ratio)

Given a multilinear polynomial $g$, and an odd function $f$ show that $\int f(x_i) \exp(-\| x \|^2) g(x-y) d x =0, \forall y,i$ where $g(x)=c$)

Integrating a product of Gaussian kernels

What does $\int_{B_r} h$ mean? Problem 3-41 in "Calculus on Manifolds" by Michael Spivak. $\int_{-\infty}^{\infty}e^{-x^2}dx=\sqrt{\pi}$.

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