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ellipke

Complete elliptic integrals of first and second kind

Syntax

K = ellipke(M)
[K,E] = ellipke(M)
[K,E] = ellipke(M,tol)

Description

K = ellipke(M) returns the complete elliptic integral of the first kind for the each element in M.

[K,E] = ellipke(M) returns the complete elliptic integral of the first and second kinds.

[K,E] = ellipke(M,tol) computes the complete elliptic integral to accuracy tol. The default is eps(class(M)); increase the tolerance for a less accurate but more quickly computed answer.

Limitations

ellipke is limited to the input domain 0 ≤ m ≤ 1.

Definitions

The complete elliptic integral of the first kind is

where m is the first argument of ellipke.

The complete elliptic integral of the second kind is

Some definitions of K and E use the elliptical modulus k or modular angle α instead of the parameter m. They are related by

References

[1] Abramowitz, M., and I.A. Stegun. Handbook of Mathematical Functions. Dover Publications, 1965.