Category:Definitions/Incomplete Elliptic Integral of the Third Kind
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This category contains definitions related to Incomplete Elliptic Integral of the Third Kind.
Related results can be found in Category:Incomplete Elliptic Integral of the Third Kind.
Definition 1
- $\ds \map \Pi {k, n, \phi} = \int \limits_0^\phi \frac {\d \phi} {\paren {1 + n \sin^2 \phi} \sqrt{1 - k^2 \sin^2 \phi} }$
is the incomplete elliptic integral of the third kind, and is a function of the variables:
- $k$, defined on the interval $0 < k < 1$
- $n \in \Z$
- $\phi$, defined on the interval $0 \le \phi \le \pi / 2$.
Definition 2
- $\ds \map \Pi {k, n, \phi} = \int \limits_0^x \frac {\d v} {\paren {1 + n v^2} \sqrt {\paren {1 - v^2} \paren {1 - k^2 v^2} } }$
is the incomplete elliptic integral of the third kind, and is a function of the variables:
Pages in category "Definitions/Incomplete Elliptic Integral of the Third Kind"
The following 5 pages are in this category, out of 5 total.