Definition of Elliptic integral. Meaning of Elliptic integral. Synonyms of Elliptic integral

Here you will find one or more explanations in English for the word Elliptic integral. Also in the bottom left of the page several parts of wikipedia pages related to the word Elliptic integral and, of course, Elliptic integral synonyms and on the right images related to the word Elliptic integral.

Definition of Elliptic integral

Elliptic integral
Integral In"te*gral, n. 1. A whole; an entire thing; a whole number; an individual. 2. (Math.) An expression which, being differentiated, will produce a given differential. See differential Differential, and Integration. Cf. Fluent. Elliptic 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.
Elliptic integral
Elliptic El*lip"tic, Elliptical El*lip"tic*al, a. [Gr. ?: cf. F. elliptique. See Ellipsis.] 1. Of or pertaining to an ellipse; having the form of an ellipse; oblong, with rounded ends. The planets move in elliptic orbits. --Cheyne. 2. Having a part omitted; as, an elliptical phrase. Elliptic chuck. See under Chuck. Elliptic compasses, an instrument arranged for drawing ellipses. Elliptic function. (Math.) See Function. Elliptic integral. (Math.) See Integral. Elliptic polarization. See under Polarization.

Meaning of Elliptic integral from wikipedia

- In integral calculus, an elliptic integral is one of a number of related functions defined as the value of certain integrals, which were first studied...
-  Complete Elliptic integral of  τ 1 X 1 ′ =  Complete Elliptic integral of  1 − τ 1 2 X 2 =  Complete Elliptic integral of  τ 2 X 2 ′ =  Complete Elliptic integral...
- to proceed to calculate the elliptic integral. Given Eq. 3 and the Legendre polynomial solution for the elliptic integral: K ( k ) = π 2 ∑ n = 0 ∞ ( (...
- named elliptic functions because they come from elliptic integrals. Those integrals are in turn named elliptic because they first were encountered for the...
- In mathematics, the Jacobi elliptic functions are a set of basic elliptic functions. They are found in the description of the motion of a pendulum, as...
- using the Arctangent Integral, also called Inverse Tangent Integral. The same procedure also works for the Complete Elliptic Integral of the second kind...
- }{2}}{\sqrt {1-x\sin ^{2}\theta }}\ d\theta } known as the complete elliptic integral of the second kind, the perimeter can be expressed in terms of that...
- which has genus zero: see elliptic integral for the origin of the term. However, there is a natural representation of real elliptic curves with shape invariant...
- S2CID 125063457. Prasolov, V.; Solovyev, Y. (1997). Elliptic Functions and Elliptic Integrals. American Mathematical Society. p. 58—60. ISBN 0-8218-0587-8...
- to integrals that generalise the elliptic integrals to all curves over the complex numbers. They include for example the hyperelliptic integrals of type...