- 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...
- 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...
-
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...
- 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 (see...
-
using the
Arctangent Integral, also
called Inverse Tangent Integral. The same
procedure also
works for the
Complete Elliptic Integral of
second kind E in...
- 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 {\displaystyle...
- to
integrals that
generalise the
elliptic integrals to all
curves over the
complex numbers. They
include for
example the
hyperelliptic integrals of type...
- quickly, it
provides an
efficient way to
compute elliptic integrals,
which are used, for example, in
elliptic filter design. The arithmetic–geometric mean...
-
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...