# Category:Complete Elliptic Integral of the First Kind

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This category contains results about **Complete Elliptic Integral of the First Kind**.

Definitions specific to this category can be found in Definitions/Complete Elliptic Integral of the First Kind.

### Definition 1

- $\ds \map K k = \int \limits_0^{\pi / 2} \frac {\d \phi} {\sqrt {1 - k^2 \sin^2 \phi} }$

is the **complete elliptic integral of the first kind**, and is a function of $k$, defined on the interval $0 < k < 1$.

### Definition 2

- $\ds \map K k = \int \limits_0^1 \frac {\d v} {\sqrt {\paren {1 - v^2} \paren {1 - k^2 v^2} } }$

is the **complete elliptic integral of the first kind**, and is a function of $k$, defined on the interval $0 < k < 1$.

## Pages in category "Complete Elliptic Integral of the First Kind"

The following 4 pages are in this category, out of 4 total.