# 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. Originally, they arose in...
- In mathematics, the Jacobi elliptic functions are a set of basic elliptic functions, and auxiliary theta functions, that are of historical importance....
- take an arbitrarily long time to fall down.) This integral can be rewritten in terms of elliptic integrals as T = 4 ℓ g F ( π 2 , sin ⁡ θ 0 2 ) {\displaystyle...
- that a contour integral around its boundary must vanish, implying that the residues of all simple poles must cancel. Historically, elliptic functions were...
- eccentricity, and the function E {\displaystyle E} is the complete elliptic integral of the second kind, E ( e ) = ∫ 0 π / 2 1 − e 2 sin 2 ⁡ θ   d θ ....
- applications in elliptic curve cryptography (ECC) and integer factorization. An elliptic curve is not an ellipse: see elliptic integral for the origin...
- to integrals that generalise the elliptic integrals to all curves over the complex numbers. They include for example the hyperelliptic integrals of type...
- {\displaystyle {\sqrt {1-x^{4}}}} (elliptic integral) 1 ln ⁡ x {\displaystyle {\frac {1}{\ln x}}} (logarithmic integral). e − x 2 {\displaystyle e^{-x^{2}}\...
- latitude μ, are unrestricted. The above integral is related to a special case of an incomplete elliptic integral of the third kind. In the notation of the...
- cir****ference of an ellipse can be expressed exactly in terms of the complete elliptic integral of the second kind. More precisely, we have C e l l i p s e = 4 a...