elliptic_e( z , m )

The incomplete elliptic integral of the second kind of z and parameter m in SageMath. Defined by

Note that all elliptic integrals in SageMath use the parameter rather than the elliptic modulus k, which is related to the parameter by $m=k^2$.

Plot on the real axis:

  show( plot( elliptic_e(x,m), x, -pi/2, pi/2, figsize=[4,2], color=(0,.5,1) ) )

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Series expansion about the origin:

show( maxima( elliptic_e(z,m) ).taylor(z,0,7) )

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Special values:

show( elliptic_e(-pi/2,m,hold=True), '=', elliptic_e(-pi/2,m) )

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Related functions:   elliptic_ec   elliptic_eu   elliptic_f   elliptic_pi

Function category: elliptic integrals sagemath-docs