Questions tagged [error-function]

Use this tag for the error and complementary error functions (erf and erfc). These are special functions formed by taking definite integrals of the Gaussian/normal distribution function.

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What is the error of a $\ln(x + R)$? [closed]

I am trying to calculate the error of a $\ln(x)$ function, given my parameter $x$ has an error $R$.
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An integral involving a Gaussian, error functions and the Owen's T function.

This question is closely related to An integral involving a Gaussian and an Owen's T function. and An integral involving error functions and a Gaussian . Let $\nu_1 \ge 1$ and $\nu_2 \ge 1$ be ...
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The Fourier transform of $\frac{\text{erf}(\omega x)}{x}$

Does anyone know the Fourier transform of $\Large\frac{\text{erf}(\omega x)}{x}$? I think it should be something like $\frac{4\pi}{k^2}\exp{(-k^2/4\omega^2)}$. Is this right? How can one go about ...
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Why this :$I(x)=\int_{-x}^x {0.5(\exp({-t² {\operatorname{erf}(t^2)}})}dt$ is not error function for $|x| >3$?

This integral : $$I(x)=\int_{-x}^x {0.5(\exp({-t² {\operatorname{erf}(t^2)}})}dt$$ close to $x$ for $|x|<3$ and converge to $1$ for $|x|>3$ from $-\infty \to +\infty$ as shown here such that ...
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Is the parity of error function enough to show :$\int_{-l}^{l} \exp ({\operatorname{-x^2erf(x)})dx=\int_{-l}^{l} \exp({\operatorname{x^2erf}}(x)})dx$?

I have tried to show the below identity using the parity of both error function and exp function but I didn't succeed, then my question here is there any analytical way to show this identity or Is ...
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Can it be proved that the integral $I_1 = \frac{1}{2}$ iff $A=0$?

I have the following integral: $$I_1= \int_{-\infty}^{\infty} \frac{d\tau}{2\pi i} \int_{-\infty}^{\infty} \frac{d\tau'}{2\pi i} \frac{1}{(\tau - i \epsilon)(\tau' - i\epsilon')}. M(\tau, \tau')$$ ...
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A quick question concerning error function

Why $\frac{1}{\sqrt{2\pi }}\int_{-\infty }^{\infty}e^{tx}e^{-x^{2}/2}dx$ equals to $e^{t^{2}/2}$ ? I know it is error function. but I just do not have any basic knowledge about error function and ...
I have two independent sets of two-dimensional measurements ($X_m^1$ and $X_m^2$) and i know their corresponding ground truth data ($X_g^1$ and $X_g^2$). So, i can calculate the error statistics for ...
Proving approximation of $\text{erf}$ with Taylor expansion
I am asked to show that $$\text{erf}(x) \approx 1 - \frac{1}{\sqrt{\pi}}\frac{1}{x}e^{-x^2}$$ in a computational project. Numerically it is really easy to show that this approximation makes sense. ...