Category:Definitions/Elliptic Integrals of the First Kind

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This category contains definitions related to Elliptic Integrals of the First Kind.
Related results can be found in Category:Elliptic Integrals of the First Kind.


Incomplete Elliptic Integral of the First Kind

$\ds \map F {k, \phi} = \int \limits_0^\phi \frac {\d \phi} {\sqrt {1 - k^2 \sin^2 \phi} }$

is the incomplete elliptic integral of the first kind, and is a function of the variables:

$k$, defined on the interval $0 < k < 1$
$\phi$, defined on the interval $0 \le \phi \le \pi / 2$.


Complete Elliptic Integral of the First Kind

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

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

Subcategories

This category has the following 2 subcategories, out of 2 total.

Pages in category "Definitions/Elliptic Integrals of the First Kind"

The following 3 pages are in this category, out of 3 total.