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Complete elliptic integral of the 3rd kind Π(n,k)

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Calculate complete elliptic integral of the 3rd kind Π(n,k).
\(\Pi(n,k)={\large\int_{\small 0}^{\frac{\pi}{2}}\frac{d\theta}{(1-nsin^2\theta)\sqrt{1-k^2sin^2\theta}}}\)
n 
k 
-1≦k≦1
\(\normalsize Complete\ elliptic\ integral\\ \hspace{120px} of\ the\ 3rd\ kind\ \Pi(n,k)\\ (1)\ \Pi(n,k)={\large\int_{\small 0}^{\frac{\pi}{2}}\frac{d\theta}{(1-nsin^2\theta)\sqrt{1-k^2sin^2\theta}}}\\ \hspace{70px}={\large\int_{\small 0}^{\small 1}\frac{dt}{(1-nt^2)\sqrt{(1-t^2)(1-k^2t^2)}}}\\\)

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