EllipticCE - Maple Help
For the best experience, we recommend viewing online help using Google Chrome or Microsoft Edge.

EllipticE

Incomplete and complete elliptic integrals of the second kind

EllipticCE

Complementary complete elliptic integral of the second kind

 Calling Sequence EllipticE(z,k) EllipticE(k) EllipticCE(k)

Parameters

 z - algebraic expression (the sine of the amplitude) k - algebraic expression (the parameter)

Description

 • The incomplete elliptic integral EllipticE is defined by

$\mathrm{EllipticE}\left(z,k\right)={\int }_{0}^{z}\frac{\sqrt{-{k}^{2}{t}^{2}+1}}{\sqrt{-{t}^{2}+1}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}ⅆt$

 • The complete elliptic integrals EllipticE and EllipticCE are defined by

$\mathrm{EllipticE}\left(k\right)=\mathrm{EllipticE}\left(1,k\right)$

$\mathrm{EllipticCE}\left(k\right)=\mathrm{EllipticE}\left(1,\sqrt{-{k}^{2}+1}\right)$

Examples

 > $\mathrm{EllipticE}\left(0.2,0.3\right)$
 ${0.2012363833}$ (1)
 > $\mathrm{EllipticE}\left(0.3\right)$
 ${1.534833465}$ (2)
 > $\mathrm{EllipticCE}\left(0.3\right)$
 ${1.096477517}$ (3)

References

 Abramowitz, M., and Stegun, I., eds. Handbook of Mathematical Functions. New York: Dover, 1972.