# 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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### Sigmoid function (Computationally Simple/Easy to Integrate)

I am working on a fitting model and I need to use a sigmoid function in the following integral $$\int_0^R S(x)\cdot x \cdot J_{0}(x) dx$$ where $S(x)$ is the sigmoid function and $J_0(x)$ is the ...
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I want to solve this integration $$\int_{-\infty}^{\infty} \mathrm{d}t \ \mathrm{erf} \Big(\frac{t-ic}{T}\Big) \ \mathrm{e}^{-\frac{(t-ib)^2}{T^2}}$$ one can open it by using integration by parts $$u ... 1answer 35 views ### error function integration \int_{0}^{\infty} \frac{x \operatorname{erf}(a x ) }{x^2+y^2} dx  [closed] I'm interested in the following integral,$$ \int_{0}^{\infty} \frac{x \operatorname{erf}(a x ) }{x^2+y^2} dx $$where, \operatorname{erf} is error function. Does the analytical solution exist to ... 0answers 37 views ### Proper name for “non-absolute” error? Suppose that we have a CDF F(x) and a model that learned this CDF, namely F_{\theta}(x). I know that the error at any point x is |F(x) - F_{\theta}(x)| (the absolute value), which is always \... 1answer 69 views ### Calculating \int_0^\infty\, e^{x^2-x} \operatorname{erfc}(x)\;dx I am trying to find$$I=\int_{0}^{\infty }{\,{{e}^{{{x}^{2}}-x}}\operatorname{erfc}\left( x \right)dx}$$where \operatorname{erfc} is the complementary error function. My Work:$${{e}^{{{x}^{2}}-x}...
I am looking for solutions to integrals of the form: $\int_{-a}^{a} \int_{-\sqrt{a^2-y^2}}^{\sqrt{a^2-y^2}}x^ny^m \exp(-ibx-idy-cx^2-cy^2)dxdy$ This is integration over the area of a circle with ...