I want to calculate the expected value to the solution of a Fokker-Plank equation, so one of the terms I got includes the complementary error function, namely: $$p(x,t|x_{0},t_{0})=\frac{B}{2 D}*e^{\frac{-Bx}{D}} * erfc(\frac{x+x_{0}-Bt}{2\sqrt{Dt}})$$

So my question is, while calculating the intergral $$E(x)=\int_{-\infty}^{\infty} x p(x,t|x_{0}t_0)$$

So I would like to know how to get aorund this integral? Is there some numerical way to calculate it, or are there even some analytical way to find ?

And of course my complementary error function is defined as: $$erfc(\frac{x+x_{0}-Bt}{2\sqrt{Dt}})=\frac{2}{\sqrt{\pi}}\int_{\frac{x+x_{0}-Bt}{2\sqrt{Dt}}}^{\infty} e^{-z^2} dz $$

Thanks in advance!


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.