elliptic integral of the first kind

elliptic integral of the first kind

[ə¦lip·tik ¦int·ə·grəl əvthə ¦fərst ‚kīnd]
(mathematics)
Any elliptic integral which is finite for all values of the limits of integration and which approaches a finite limit when one of the limits of integration approaches infinity.
References in periodicals archive ?
The incomplete elliptic integral of the first kind F is defined as
In terms of the Gauss hypergeometric function, the complete elliptic integral of the first kind can be expressed as
where L is the incomplete elliptic integral of the first kind, k is its modulus, and [psi] is its amplitude.
A series expansion of an elliptic or hyperelliptic integral in elementary symmetric functions is given, illustrated with numerical coefficients for terms through degree seven for the symmetric elliptic integral of the first kind.
Complete elliptic integral of the first kind is defined as Elliptic Integrals are said to be complete when the amplitude
Begin by introducing the elliptic integral of the first kind

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