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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
Jul
5
comment Conditions for differentiation under integral sign
I'm not affraid, I just needed to be sure :-) Thanks!
Jul
5
comment Conditions for differentiation under integral sign
Thank you, you're obviously right. But if my integration interval was $(-\infty,+\infty)$ – how should I manage that? Define $g(x)$ for $(-\infty,0)$ and $[0,+\infty)$ separately?
Jul
5
asked Conditions for differentiation under integral sign
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)
May
28
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 $
added 167 characters in body
May
3
comment 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 $
Thanks Dilip. I did calculations you suggested but unfortunately I can’t see how this result is supposed to help me. With $c\neq 0$ I still have integrand $\exp\left(-a^2 (-d + x)^2\right) \mathrm{erf}\left(b (x-c)\right) \mathrm{erf}\left(a (x-d)\right)$ and I don’t know how to proceed with it.
May
3
answered 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 $
Apr
29
awarded  Supporter
Apr
29
accepted Integral with exp and erf