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

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

 $\Pi(\phi,n,k)={\large\int_{\small 0}^{\hspace{25}\phi}\frac{d\theta}{(1-nsin^2\theta)\sqrt{1-k^2sin^2\theta}}}$

 φ degree   -360≦φ≦360radian    -2π≦φ≦2π n k -1≦k≦1 6digit10digit14digit18digit22digit26digit30digit34digit38digit42digit46digit50digit
 ・ Π(x,n,k) can be used at x=sin(φ).$\normal Incomplete\ elliptic\ integral\\\hspace{100} of\ the\ 3rd\ kind\ \Pi(\phi,n,k)\\[10](1)\ \Pi(\phi,n,k)={\large\int_{\small 0}^{\hspace{25}\phi}\frac{d\theta}{(1-nsin^2\theta)\sqrt{1-k^2sin^2\theta}}}\\\hspace{80}={\large\int_{\small 0}^{\hspace{25}\small x}\frac{dt}{(1-nt^2)\sqrt{(1-t^2)(1-k^2t^2)}}}\\\hspace{230}x=sin\phi\\$

Incomplete elliptic integral of the 3rd kind Π(φ,n,k)
 [1-1] /1 Disp-Num5103050100200
[1]  2010/05/25 09:26   Male / 40 level / A researcher / Very /
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