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# scipy.special.ellipe¶

scipy.special.ellipe(m) = <ufunc 'ellipe'>

Complete elliptic integral of the second kind

This function is defined as

$E(m) = \int_0^{\pi/2} [1 - m \sin(t)^2]^{1/2} dt$
Parameters: m : array_like Defines the parameter of the elliptic integral. E : ndarray Value of the elliptic integral.

ellipkm1
Complete elliptic integral of the first kind, near m = 1
ellipk
Complete elliptic integral of the first kind
ellipkinc
Incomplete elliptic integral of the first kind
ellipeinc
Incomplete elliptic integral of the second kind

Notes

Wrapper for the Cephes [R402] routine ellpe.

For m > 0 the computation uses the approximation,

$E(m) \approx P(1-m) - (1-m) \log(1-m) Q(1-m),$

where $$P$$ and $$Q$$ are tenth-order polynomials. For m < 0, the relation

$E(m) = E(m/(m - 1)) \sqrt(1-m)$

is used.

References

 [R402] (1, 2) Cephes Mathematical Functions Library, http://www.netlib.org/cephes/index.html