info prev up next book cdrom email home

Elliptic Integral Singular Value k2

The second Singular Value $k_2$, corresponding to

\begin{displaymath}
K'(k_2)=\sqrt{2}\,K(k_2),
\end{displaymath} (1)

is given by
$\displaystyle k_2$ $\textstyle =$ $\displaystyle \tan\left({\pi\over 8}\right)=\sqrt{2}-1,$ (2)
$\displaystyle k_2'$ $\textstyle =$ $\displaystyle \sqrt{2}\,(\sqrt{2}-1).$ (3)

For this modulus,
\begin{displaymath}
E(\sqrt{2}-1)={1\over 4}\sqrt{\pi\over 4}\left[{{\Gamma({\te...
...style{5\over 8}})\over\Gamma({\textstyle{9\over 8}})}}\right].
\end{displaymath} (4)




© 1996-9 Eric W. Weisstein
1999-05-25