Category:Complete Elliptic Integral of the Third Kind
Jump to navigation
Jump to search
This category contains results about Complete Elliptic Integral of the Third Kind.
Definitions specific to this category can be found in Definitions/Complete Elliptic Integral of the Third Kind.
Definition 1
- $\ds \map \Pi {k, n} = \int \limits_0^{\pi / 2} \frac {\d \phi} {\paren {1 + n \sin^2 \phi} \sqrt {1 - k^2 \sin^2 \phi} }$
is the complete elliptic integral of the third kind, and is a function of the variables:
- $k$, defined on the interval $0 < k < 1$
- $n \in \Z$
Definition 2
- $\ds \map \Pi {k, n} = \int \limits_0^1 \frac {\d v} {\paren {1 + n v^2} \sqrt {\paren {1 - v^2} \paren {1 - k^2 v^2} } }$
is the complete elliptic integral of the third kind, and is a function of the variables:
- $k$, defined on the interval $0 < k < 1$
- $n \in \Z$
Pages in category "Complete Elliptic Integral of the Third Kind"
This category contains only the following page.