# Elliptic integral

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Related to Elliptic integral: elliptic integral of the second kind
 (Math.) See Integral. one of an important class of integrals, occurring in the higher mathematics; - so called because one of the integrals expresses the length of an arc of an ellipse.

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1,2] are the outer and inner parts of the total contour, respectively; K(k) is the complete elliptic integral of the first kind of module k [9];
i]), where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is elliptic integral of the first kind, [sin.
The incomplete elliptic integral produced for the ellipsoid can be evaluated using the Maple EllipticE command.
However, with the appropriate reduction formula, every elliptic integral can be brought into a form that involves integrals over rational functions and the three Legendre canonical forms (i.
e0])) are the complete elliptic integral of first kind with the modulus [k.
j] is the complete elliptic integral of the first kind, and cd is Jacobi elliptic function.
First, its arc length should be given by an elliptic integral, say [integral] dx/ [square root of p(x)] for a certain polynomial p.
0]) and [alpha] = 4K([beta])/[lambda], and K([beta]) is the complete elliptic integral of first kind.
A faster than quadratically convergent series is given for numerical computation of the complete symmetric elliptic integral of the third kind.
2] - 1 (12) can be transformed in the elliptic integral of the first kind F ([sigma],[p.
where, k(p[prime]) is the complete elliptic integral of first kind, p[prime] = [square root of 1 - [p.
Complete elliptic integral of the first kind is defined as Elliptic Integrals are said to be complete when the amplitude

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