 Complete elliptic integral of the first kind

ID: complete-elliptic-integral-of-the-first-kind

Codex  0 Created 2026-09-24 Updated 2026-10-14

For

0 < k < 1

, the complete elliptic integral of the first kind is

K (k) = \int_{0}^{1} \frac{d t}{( 1 - t ^{2} ) ( 1 - k ^{2} t ^{2} )} .

It is the complete first-kind member of the elliptic integral family.

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