- #1
petru
- 6
- 0
Hi,
I've been trying to evaluate the following integral
[tex] \int_{z}^{\infty}\exp\left(-y^{2}\right)\mathrm{erf}\left(b\left(y-c\right)\right)\,\mathrm{d}y [/tex]
or equivalently
[tex] \int_{z}^{\infty}\exp\left(-y^{2}\right)\mathrm{erfc}\left(b\left(y-c\right)\right)\,\mathrm{d}y [/tex]
[tex]\mathrm{erf}\left(x\right)=\frac{2}{\sqrt{\pi}} \int_{0}^{x}\exp\left(-u^{2}\right)\,\mathrm{d}u, \quad\quad \mathrm{erfc}\left(x\right)=1-\mathrm{erf}\left(x\right)=\frac{2}{\sqrt{\pi}} \int_{x}^{+\infty}\exp\left(-u^{2}\right)\,\mathrm{d}u[/tex]
I guess I tried to employ all techniques I'm familiar with but with no result.
Can anyone help me with this one, please?
Thank you!
I've been trying to evaluate the following integral
[tex] \int_{z}^{\infty}\exp\left(-y^{2}\right)\mathrm{erf}\left(b\left(y-c\right)\right)\,\mathrm{d}y [/tex]
or equivalently
[tex] \int_{z}^{\infty}\exp\left(-y^{2}\right)\mathrm{erfc}\left(b\left(y-c\right)\right)\,\mathrm{d}y [/tex]
[tex]\mathrm{erf}\left(x\right)=\frac{2}{\sqrt{\pi}} \int_{0}^{x}\exp\left(-u^{2}\right)\,\mathrm{d}u, \quad\quad \mathrm{erfc}\left(x\right)=1-\mathrm{erf}\left(x\right)=\frac{2}{\sqrt{\pi}} \int_{x}^{+\infty}\exp\left(-u^{2}\right)\,\mathrm{d}u[/tex]
I guess I tried to employ all techniques I'm familiar with but with no result.
Can anyone help me with this one, please?
Thank you!
Last edited: