Question

$\int_{-\infty}^{+\infty}\phi\left(x\right)\Phi\left(\frac{a}{\mathrm{e}^x}\right)dx=\Phi\left(\frac{a}{\sqrt{2}}\right)$

score 193 · Answer 1 · 2015-08-09 10:44:51

193

Views

$\int_{-\infty}^{+\infty}\phi\left(x\right)\Phi\left(\frac{a}{\mathrm{e}^x}\right)dx=\Phi\left(\frac{a}{\sqrt{2}}\right)$

Published on 09 Aug 2015 - 10:44

score 177 · Answer 2 · 2015-08-10 19:32:45

177

Views

Simplifying integral:$\int_{0}^{\infty}{\exp\left(-\left(u^2+{ {\alpha^2}\over {16u^2t}}\right)\right)}~\mathrm{d}u$

Published on 10 Aug 2015 - 19:32

score 627 · Answer 3 · 2015-08-11 12:32:23

627

Views

Solve: $\int_{0}^{\infty}{ \left( \cos \left( ... \right)+\sin \left( ... \right) \right) \frac{e^{-u^2}}{(u^2+ \frac{\alpha}{4t})^2} }~\mathrm{d}u$

Published on 11 Aug 2015 - 12:32

score 93 · Answer 4 · 2015-08-11 12:54:05

93

Views

Solve:$\int_{0}^{t}{{\left(\cos({...})+\sin({...})\right)} \frac{\lambda^2 e^{(...)}}{\sqrt{\pi (t-r)}} \text{Erfc}{\left(... \right)} }~\mathrm{d}r$

Published on 11 Aug 2015 - 12:54

score 595 · Answer 5 · 2015-08-12 10:29:32

595

Views

Multivariate Gaussian integral of ratio of quadratic forms

Published on 12 Aug 2015 - 10:29

score 29 · Answer 6 · 2026-03-26 01:14:54

29

Views

Gauss Numerical Integration Verification and Help

Published on 26 Mar 2026 - 1:14

score 73 · Answer 7 · 2026-03-26 01:09:15

73

Views

Gaussian Integration verification

Published on 26 Mar 2026 - 1:09

score 82 · Answer 8 · 2015-08-20 14:58:04

82

Views

Evaluation on a basis of gaussian integral

Published on 20 Aug 2015 - 14:58

score 1.3k · Answer 9 · 2015-08-28 16:26:57

1.3k

Views

Result of $\int \limits_{-\infty}^{+\infty}x^2\times\exp\left(\dfrac{-x^2}{2}\right)\mathrm{d}x$

Published on 28 Aug 2015 - 16:26

score 152 · Answer 10 · 2015-09-01 05:25:56

152

Views

Evaluate the integral $\int_0^{\infty} e^{\frac{-t(s-1)^2}{2}} \left( \frac{t(s-1)^3}{3} \right) ds$

Published on 01 Sep 2015 - 5:25

score 1.4k · Answer 11 · 2015-09-13 11:38:49

1.4k

Views

Direct evaluation of Multivariate Complex Gaussian Integral without using analytic continuation

Published on 13 Sep 2015 - 11:38

score 178 · Answer 12 · 2015-09-16 15:20:37

178

Views

Limit of $\frac{1}{x}\int_{x}^{2x}e^{-t^2}dt$ when $x\to0$

Published on 16 Sep 2015 - 15:20

score 2.2k · Answer 13 · 2015-09-22 04:48:26

2.2k

Views

Fourier transform of a truncated Gaussian function

Published on 22 Sep 2015 - 4:48

score 1k · Answer 14 · 2026-03-26 07:32:29

1k

Views

Integrating:$\int\limits_0 ^ {\infty}e^{-x^2}\ln(x)dx $

Published on 26 Mar 2026 - 7:32

score 94 · Answer 15 · 2015-09-30 22:45:03

94

Views

Equation involving an error and Gaussian functions

Published on 30 Sep 2015 - 22:45

List Question

$\int_{-\infty}^{+\infty}\phi\left(x\right)\Phi\left(\frac{a}{\mathrm{e}^x}\right)dx=\Phi\left(\frac{a}{\sqrt{2}}\right)$

Simplifying integral:$\int_{0}^{\infty}{\exp\left(-\left(u^2+{ {\alpha^2}\over {16u^2t}}\right)\right)}~\mathrm{d}u$

Solve: $\int_{0}^{\infty}{ \left( \cos \left( ... \right)+\sin \left( ... \right) \right) \frac{e^{-u^2}}{(u^2+ \frac{\alpha}{4t})^2} }~\mathrm{d}u$

Solve:$\int_{0}^{t}{{\left(\cos({...})+\sin({...})\right)} \frac{\lambda^2 e^{(...)}}{\sqrt{\pi (t-r)}} \text{Erfc}{\left(... \right)} }~\mathrm{d}r$

Multivariate Gaussian integral of ratio of quadratic forms

Gauss Numerical Integration Verification and Help

Gaussian Integration verification

Evaluation on a basis of gaussian integral

Result of $\int \limits_{-\infty}^{+\infty}x^2\times\exp\left(\dfrac{-x^2}{2}\right)\mathrm{d}x$

Evaluate the integral $\int_0^{\infty} e^{\frac{-t(s-1)^2}{2}} \left( \frac{t(s-1)^3}{3} \right) ds$

Direct evaluation of Multivariate Complex Gaussian Integral without using analytic continuation

Limit of $\frac{1}{x}\int_{x}^{2x}e^{-t^2}dt$ when $x\to0$

Fourier transform of a truncated Gaussian function

Integrating:$\int\limits_0 ^ {\infty}e^{-x^2}\ln(x)dx $

Equation involving an error and Gaussian functions

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