# Incomplete elliptic integral of the 1st kind F(φ,k) Calculator

## Calculates the incomplete elliptic integral of the first kind F(φ,k).

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

 φ degree   -360≦φ≦360radian    -2π≦φ≦2π k -1≦k≦1 6digit10digit14digit18digit22digit26digit30digit34digit38digit42digit46digit50digit
 ・ F(x,k) can be used at x=sin(φ).$\normal Incomplete\ elliptic\ integral\\\hspace{120} of\ the\ 1st\ kind\ F(\phi,k)\\[10](1)\ F(\phi,k)={\large\int_{\small 0}^{\hspace{25}\small\phi}\frac{d\theta}{\sqrt{1-k^2sin^2\theta}}}\\\hspace{70}={\large\int_{\small 0}^{\hspace{25}\small x}\frac{dt}{\sqrt{(1-t^2)(1-k^2t^2)}}}\ ,\hspace{10}x=sin\phi\\$

Incomplete elliptic integral of the 1st kind F(φ,k)
 [1-3] /3 Disp-Num5103050100200
[1]  2014/06/01 22:37   Male / 60 years old level or over / A teacher / A researcher / Very /
Purpose of use
Check some maths I posted on Wikipedia.
[2]  2011/09/02 02:09   Male / 40 years old level / A teacher / A researcher / Very /
Purpose of use
for research
Comment/Request
excellent
[3]  2009/11/11 05:02   Male / 50 level / A researcher / Very /
Purpose of use
testing own code
Comment/Request
I am happy with this tool.

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