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

## Calculates the complete elliptic integral of the third kind Π(n,k).

 $\Pi(n,k)={\large\int_{\small 0}^{\hspace{25}\frac{\pi}{2}}\frac{d\theta}{(1-nsin^2\theta)\sqrt{1-k^2sin^2\theta}}}$
 n k -1≦k≦1
 6dgt10dgt14dgt18dgt22dgt26dgt30dgt34dgt38dgt42dgt46dgt50dgt
 $\normal Complete\ elliptic\ integral\\\hspace{120} of\ the\ 3rd\ kind\ \Pi(n,k)\\[10](1)\ \Pi(n,k)={\large\int_{\small 0}^{\hspace{25}\frac{\pi}{2}}\frac{d\theta}{(1-nsin^2\theta)\sqrt{1-k^2sin^2\theta}}}\\\hspace{70}={\large\int_{\small 0}^{\hspace{25}\small 1}\frac{dt}{(1-nt^2)\sqrt{(1-t^2)(1-k^2t^2)}}}\\$

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