- 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...
- 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...
- to
proceed to
calculate the
elliptic integral.
Given Eq. 3 and the
Legendre polynomial solution for the
elliptic integral: K(k)=π2∑n=0∞((2n−1)!!(2n)!...
-
named elliptic functions because they come from
elliptic integrals.
Those integrals are in turn
named elliptic because they
first were
encountered for the...
-
using the
Arctangent Integral, also
called Inverse Tangent Integral. The same
procedure also
works for the
Complete Elliptic Integral of the
second kind...
-
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...
- eccentricity, and the
function E{\displaystyle E} is the
complete elliptic integral of the
second kind, E(e)=∫0π/21−e2sin2θ dθ{\displaystyle E(e)\,=\...
- quickly, it
provides an
efficient way to
compute elliptic integrals,
which are used, for example, in
elliptic filter design. The arithmetic–geometric mean...
- to
integrals that
generalise the
elliptic integrals to all
curves over the
complex numbers. They
include for
example the
hyperelliptic integrals of type...
-
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...