Category:Complete Elliptic Integrals
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This category contains results about Complete Elliptic Integrals.
Definitions specific to this category can be found in Definitions/Complete Elliptic Integrals.
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 $0 < k < 1$.
Complete Elliptic Integral of the Second Kind
- $\ds \map E k = \int \limits_0^{\pi / 2} \sqrt {1 - k^2 \sin^2 \phi} \rd \phi$
is the complete elliptic integral of the second kind, and is a function of $k$, defined on the interval $0 < k < 1$.
Complete Elliptic Integral of the Third Kind
- $\ds \map \Pi {k, n} = \int \limits_0^{\pi / 2} \frac {\d \phi} {\paren {1 + n \sin^2 \phi} \sqrt {1 - k^2 \sin^2 \phi} }$
is the complete elliptic integral of the third kind, and is a function of the variables:
- $k$, defined on the interval $0 < k < 1$
- $n \in \Z$
Subcategories
This category has the following 3 subcategories, out of 3 total.