# 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 6digit10digit14digit18digit22digit26digit30digit34digit38digit42digit46digit50digit
 $\normal Complete\ elliptic\ integral\\\hspace{120} of\ the\ 3rd\ kind\ \Pi(n,k)\\[10](1)\ \Pi(n,k)={\large\int_{\small 0}^{\hspace{25}\frac{\pi}{2}}\frac{d\theta}{(1-nsin^2\theta)\sqrt{1-k^2sin^2\theta}}}\\\hspace{70}={\large\int_{\small 0}^{\hspace{25}\small 1}\frac{dt}{(1-nt^2)\sqrt{(1-t^2)(1-k^2t^2)}}}\\$

Complete elliptic integral of the 3rd kind Π(n,k)
 [1-2] /2 Disp-Num5103050100200
[1]  2013/03/16 18:06   Male / 50 years old level / A teacher / A researcher / Not at All /
Purpose of use
To verify some Matlab code
Comment/Request
The first try (.5,.5) is way different than the result from my code or from Wolfram Mathematica's web site calculator, which agree with each other.
from Keisan
The function definition is different.
keisan: Π(n,k)=integral(0,1){dt/(1-n*t^2)/sqrt((1-t^2)(1-k^2*t^2))}
Wolfram: Π(n,m)=integral(0,1){dt/sqrt((1-t^2)(1-m*t^2))}
Therefor if convert k=sqrt(m), the same answer.
[2]  2009/09/15 06:26   Male / 50 level / SOHO / Very /
Purpose of use
checking calculation results
Comment/Request
slow so ok for single calculations. looks like it uses a c++ library on the back end. would be faster if the script was on the page

Sending completion

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