EllipticE - Maple Programming Help

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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.