O'Reilly logo

Table of Integrals, Series, and Products, 8th Edition by Daniel Zwillinger

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

8

Special Functions

8.1 Elliptic Integrals and Functions

8.11 Elliptic integrals

8.110

1. Every integral of the form R(x,P(x))dxsi1_e, where P(x) is a third- or fourth-degree polynomial, can be reduced to a linear combination of integrals leading to elementary functions and the following three integrals:

dx(1x2)(1k2x2),(1k2x2)(1x2)dx,dx(1nx2)(1x2)(1k2x2),

si2_e

which are called respectively elliptic integrals of the first, second, and third kind in the Legendre normal form. The results of this reduction for the more frequently encountered ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required