# Tagged Questions

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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### Weber-type integral

In connection with this answer, I came across the following integral: $$\int_{0}^{\infty} \frac{du}{u} \: \,e^{-t u^2} \frac{J_0(u) Y_0(r u)-J_0(r u) Y_0(u)}{J_0^2(u)+Y_0^2(u)}$$ where $r \gt 1$. I ...
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### Non-trivial values of error function $\operatorname{erf}(x)$?

The so called error function $\operatorname{erf}(x)$ is defined as $$\operatorname{erf}(x)=\frac{2}{\sqrt{\pi}}\int_0^x e^{-t^2}dt,$$ and it is well known that $\operatorname{erf}(\infty)=1$. Are ...
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### Understanding Variance

I have to analyse the reasons that we did not meet target. Our target is 4750 m Our target speed is 500m/hr Our target hrs are 9.5 We achieved a speed of 550 m/hr We achieved hrs of 9.1 We achieved ...
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### Integration involving Error function

I am interested in the following integral $$\int_0^\infty x^n\text{Erf}[ax]j_m(bx)dx,$$ where Erf is the error function $j_n$ is the spherical Bessel function of first kind. Does the analytical ...
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### How are subtraction operations better conditioned than addition?

I was reading about error analysis in numerical methods, particularly about calculating the sum of arrays. I understand how naively summing all elements can lead to accumulation of error especially ...
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### Existence of solution for equation with erfc

I'm looking for the self-consistent (e.g. input needs to be the same as output) solution of $r$ in $$r = \frac{1}{2}\operatorname{erfc}(z(r))$$ where $\operatorname{erfc}$ is complimentary error ...
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### Show that this conversion between $\Phi$ and erf(z) holds for all z

I am trying to wrap my head around the connections between the standard Normal distribution and the error function. I could use some help working through the following problem. Show that the ...
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### Is the Taylor Expansion a good approximation

Say I use a computer to sum the first 26 terms of $e^{-5}$ (degree 25), will this taylor expansion provide a good approximation? It summed to $.0067$ To me this seems like a good approximation, but I ...