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Mar
3
awarded  Commentator
Mar
3
comment Erf squared approximation
Thanks a lot @Claude Leibovici for valuable insight into the approximation. I will clarify though that I'm not interested in the best approximation possible. In fact I need to use it to evaluate some integrals with erf squared, and my approximation seems more convenient (you can check my older posts). And BTW, could you explain what REIS is?
Mar
3
awarded  Curious
Mar
2
comment Erf squared approximation
Thanks Jack D'Aurizio. I need to digest your answer first but for now I can say that I know the approximation $\operatorname{erf}(x)^2 \approx 1-e^{-4x^2/\pi}$ but my is better. FYI the least-squares method gives $\rho^{2}=1.239$, but I find $\rho^{2}=\pi^{2}/8=1.2337$ more elegant, if I might say so :-)
Mar
2
asked Erf squared approximation
Sep
30
comment Integral of the product of squared exponential and two erf functions
I'm not sure if you noticed my comment under your original post so I put it here once again because I'm really curious about your field of research and where that "lovely" integral appeared :-)
Sep
29
answered Integral of the product of squared exponential and two erf functions
Sep
24
awarded  Autobiographer
Apr
27
revised Evaluating $ \int_{-\infty}^{\infty}x\exp\left(-b^{2}\left(x-c\right)^{2}\right)\mathrm{erf}^{2}\left(a\left(x-d\right)\right)\,\mathrm{d}x $
edited tags
Apr
27
revised Integral of product of exponential function and two complementary error functions (erfc)
edited tags
Apr
27
revised Differentiation under integral sign
edited tags
Apr
22
revised Integral of product of exponential function and two complementary error functions (erfc)
added 660 characters in body
Apr
21
comment Differentiation under integral sign
@OmranKouba Right, so it was a silly mistake after all. But now it turns out I cannot evaluate the integral. I have been struggling with similar integrals for quite some time now and I'm out of ideas. Is there some kind of explaination why the integral with infinite limits "works", but when I change the lower limit to zero, it seems undoable. Maybe it is not a valid question but I am really curious since I am not a trained mathematician.
Apr
21
asked Differentiation under integral sign
Apr
15
revised Integral of product of exponential function and two complementary error functions (erfc)
added 664 characters in body
Oct
3
awarded  Fanatic
Jul
25
awarded  Enthusiast
Jun
10
answered Integral of product of exponential function and two complementary error functions (erfc)
Jun
9
revised Integral of product of exponential function and two complementary error functions (erfc)
edited title
Jun
9
asked Integral of product of exponential function and two complementary error functions (erfc)