Formula:6946

Digital Library of Mathematical Functions ID 19.9.E7

{\displaystyle{\displaystyle(1-\tfrac{1}{4}k^{2})^{-1/2}<\frac{4}{\pi k^{2}}(E% \left(k\right)-{k^{\prime}}^{2}K\left(k\right))<\min((k^{\prime})^{-1/4},4/\pi% ),}}

Constraint(s)

${\displaystyle{\displaystyle\pi}}$ : the ratio of the circumference of a circle to its diameter
${\displaystyle{\displaystyle K\left(\NVar{k}\right)}}$ : Legendre’s complete elliptic integral of the first kind
${\displaystyle{\displaystyle E\left(\NVar{k}\right)}}$ : Legendre’s complete elliptic integral of the second kind
${\displaystyle{\displaystyle k}}$ : real or complex modulus
${\displaystyle{\displaystyle k^{\prime}}}$ : complementary modulus

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