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MATLAB Function Reference Volume 1: A - E - Bad Request

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ellipke<br />

Algorithm ellipke computes the complete elliptic integral using the method of the<br />

arithmetic-geometric mean described in [1], section 17.6. It starts with the<br />

triplet of numbers<br />

2-484<br />

a 0<br />

ellipke computes successive iterations of ai , bi , and ci with<br />

stopping at iteration n when cn≈0, within the tolerance specified by eps. The<br />

complete elliptic integral of the first kind is then<br />

Limitations ellipke is limited to the input domain 0 ≤ m ≤<br />

1 .<br />

See Also ellipj<br />

= 1,<br />

b0 ( 1 – m)<br />

1<br />

--<br />

= 2,<br />

c0 ( m)<br />

1<br />

--<br />

= 2<br />

ai bi =<br />

1<br />

-- ( a<br />

2 i – 1 + bi – 1)<br />

( ai – 1bi<br />

– 1)<br />

1<br />

=<br />

--<br />

2<br />

ci =<br />

1<br />

-- ( a<br />

2 i – 1 – bi – 1)<br />

K( m)<br />

=<br />

π<br />

---------<br />

2an <strong>Reference</strong>s [1] Abramowitz, M. and I.A. Stegun, Handbook of Mathematical <strong>Function</strong>s,<br />

Dover Publications, 1965, 17.6.

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