List questions from error-function

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Arctan(f(x)) is almost the same as Erf(f(x)) for many f(x). Is the just coincidence or is there a reason?

Published on 13 Apr 2026 - 21:23

52

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If $y$ is the solution of $\left\{y'=-y+\sqrt{t},y(0)=y_0>0\right\}$, then $\lim_{t\to\infty}\frac{y(t)}{\sqrt{t}}=1$

Published on 16 Apr 2026 - 7:33

113

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probability: When $X\sim\mathcal{N}(\mu, \sigma^2)$, the med = $\mu$

Published on 13 Apr 2026 - 5:03

38.5k

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How to integrate $e^{-x^2 -y^2}$?

Published on 10 May 2026 - 8:53

48

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Why is the Wronskian of these two functions equal to $\frac{2}{\sqrt{\pi}}$

Published on 16 Apr 2026 - 6:02

247

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Integral of a gaussian over a slice of the plane

Published on 14 Apr 2026 - 0:24

431

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Gauss Quadrature Error in 2D

Published on 16 Apr 2026 - 0:41

10.3k

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finding Laplace transform of $\operatorname{erf}(\sqrt{t})$

Published on 15 Apr 2026 - 9:22

461

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Relationship between incomplete gamma function and error function

Published on 09 Apr 2026 - 9:00

188

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Erf/gaussian integral

Published on 08 Apr 2026 - 22:51

1.7k

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Analytical Solution for 1D Heat Diffusion on Cylindrical/Spherical Coordinates

Published on 11 May 2026 - 1:01

107

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Maclaurin Series for $\operatorname{erf}(z)$

Published on 15 Apr 2026 - 12:51

126

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Asymptotic of $I(x)=\int_{-\infty}^{x} \exp(-t^2 \operatorname {erfi}(t \sqrt{2\pi}) \operatorname {erf}(t \sqrt{2\pi})) dt$ for $x\to \infty$?

Published on 16 Apr 2026 - 13:07

1.4k

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Integrals involving Gaussian Q function

Published on 14 Apr 2026 - 7:49

117

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How to integrate the following expression?

Published on 09 Apr 2026 - 6:15

List Question

Arctan(f(x)) is almost the same as Erf(f(x)) for many f(x). Is the just coincidence or is there a reason?

If $y$ is the solution of $\left\{y'=-y+\sqrt{t},y(0)=y_0>0\right\}$, then $\lim_{t\to\infty}\frac{y(t)}{\sqrt{t}}=1$

probability: When $X\sim\mathcal{N}(\mu, \sigma^2)$, the med = $\mu$

How to integrate $e^{-x^2 -y^2}$?

Why is the Wronskian of these two functions equal to $\frac{2}{\sqrt{\pi}}$

Integral of a gaussian over a slice of the plane

Gauss Quadrature Error in 2D

finding Laplace transform of $\operatorname{erf}(\sqrt{t})$

Relationship between incomplete gamma function and error function

Erf/gaussian integral

Analytical Solution for 1D Heat Diffusion on Cylindrical/Spherical Coordinates

Maclaurin Series for $\operatorname{erf}(z)$

Asymptotic of $I(x)=\int_{-\infty}^{x} \exp(-t^2 \operatorname {erfi}(t \sqrt{2\pi}) \operatorname {erf}(t \sqrt{2\pi})) dt$ for $x\to \infty$?

Integrals involving Gaussian Q function

How to integrate the following expression?

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