Encyclopedia > Elliptic integral

  Article Content

Elliptic integral

An elliptic integral is any function f which can be expressed in the form

<math> f(x) = \int_{c}^{x} R(t,P(t))\ dt </math>

where R is a rational function of its two arguments, P is the square root of a polynomial of degree 3 or 4 with no repeated roots, and c is a constant.

Particular examples include:

  • The complete elliptic integral of the first kind K is defined as
<math> K(x) = \int_{0}^{1} \frac{1}{ \sqrt{(1-t^2)(1-x^2 t^2)} }\ dt </math>
and can be computed in terms of the arithmetic-geometric mean.

  • The complete elliptic integral of the second kind E is defined as
<math> E(x) = \int_{0}^{1} \frac{ \sqrt{1-x^2 t^2} }{ \sqrt{1-t^2} }\ dt </math>



All Wikipedia text is available under the terms of the GNU Free Documentation License

 
  Search Encyclopedia

Search over one million articles, find something about almost anything!
 
 
  
  Featured Article
Ludvika

... Ludvika (http://www.ludvika.se) - Official site Municipalities of Dalarna[?]: Avesta  |  Borlänge  |  Falun  |  Gagnef ...

 
 
 
This page was created in 60.4 ms