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Complete elliptic integral of the first kind $K(m)$
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Numbers
$m$ 
$K(m)$
INPUT{numbers.yaml} (not shown in preview)
Definition
The list contains the evaluations of the complete elliptic integral of the first kind $K(m) = \int_0^1 \frac{dt}{\sqrt{(1-t^2)(1-mt^2)}}$ for some parameters $m=k^2$, where $k$ is the ellpitic modulus.
Parameters
$m$
—   real number ($0\leq m < 1$)
Formulas
(1)
$K(m) = \int_0^{\pi/2} \frac{d\theta}{\sqrt{1-m\sin^2\theta}}$.
Comments
(2)
$K(m)$ is also denoted as $K(k)$ despite the relation $m=k^2$ between the parameter $m$ and the elliptic modulus $k$.
Links
Data properties
Entries are of type: real number
Table is complete: no