integration - Asymptotic expansion of complete elliptic integral of third kind

Is there a way to compute the expansion of the complete elliptic integral of third kind

$\Pi(n,k)=\int_0^{\pi/2} \frac{d\varphi}{(1-n\sin^2\varphi)\sqrt{1-k^2\sin^2\varphi}}$

for

$\Pi(1+\epsilon,1-\epsilon)\ , \qquad \epsilon\to 0$,

and if so, what is it?