Originally Posted by

**wclayman** when reading a paper, the author said that

$\displaystyle y(t) = Ur(t)\int_{-\infty}^t dt^\prime \exp\left(-\frac{t-t^\prime}{\tau} - U\int_{t^\prime}^t d t^{\prime\prime} r(t^{\prime\prime})\right)$

can be expanded as expression involving $\displaystyle r(t), r^\prime(t) ... $

(if $\displaystyle r^\prime / r \ll r $)

$\displaystyle y(t) \approx \frac{r}{1+rU\tau} +r^\prime\frac{Ur\tau^2}{(1+rU\tau)^3} + \cdots $,

I don't know how he arrived at this conclusion. Can anyone enlighten me with some suggestions?