Question

Gaussian type integral $\int_{-\infty}^{\infty} \frac{\mathrm{e}^{-a^2 x^2}}{1 + x^2} \mathrm{d}x$

score 633 · Answer 1 · 2026-03-28 22:26:33

633

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Gaussian type integral $\int_{-\infty}^{\infty} \frac{\mathrm{e}^{-a^2 x^2}}{1 + x^2} \mathrm{d}x$

Published on 28 Mar 2026 - 22:26

score 1.2k · Answer 2 · 2017-11-30 16:49:09

1.2k

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score 296 · Answer 3 · 2017-12-04 17:19:00

296

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score 1.7k · Answer 4 · 2017-12-20 21:41:29

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score 804 · Answer 5 · 2026-03-29 00:06:41

804

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score 6.8k · Answer 6 · 2011-09-19 03:29:29

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score 986 · Answer 7 · 2012-04-27 11:26:05

986

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score 896 · Answer 8 · 2012-05-10 13:27:39

896

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score 2.7k · Answer 9 · 2012-06-09 13:26:34

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1.1k

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score 1.6k · Answer 11 · 2012-08-29 18:47:43

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score 658 · Answer 12 · 2012-09-20 06:16:48

658

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421

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score 698 · Answer 15 · 2013-03-28 20:00:01

698

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List Question

Gaussian type integral $\int_{-\infty}^{\infty} \frac{\mathrm{e}^{-a^2 x^2}}{1 + x^2} \mathrm{d}x$

What is a good approximation for the inverse of the cumulative distribution function?

Absolute Value of Error Function

defining inverse error function

Analytic solution for integral of Gaussian and error functions

How to compute $ \int_0^1 {e^{-x^2}} dx$

Evaluating $ \int_{-\infty}^{\infty}x\exp\left(-b^{2}\left(x-c\right)^{2}\right)\mathrm{erf}^{2}\left(a\left(x-d\right)\right)\,\mathrm{d}x $

Integrating a product of exponential and complementary error function with square-root of variable in the denominator

Integral of product of exponential function and two complementary error functions (erfc)

Evaluation of $\sum_{n=1}^\infty \frac{1}{\Gamma (n+s)}$

What is the significance of error function?

Integral of two error functions (erf)

How to prove error function $\mbox{erf}$ is entire (i.e., analytic everywhere)?

Advice on an integral involving the error function

Nonlinear method to solve an equation with the error function in it

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