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

5

Indefinite Integrals of Special Functions

5.1 Elliptic Integrals and Functions

Notation: k=1k2(cf. 8.1).si1_e

5.11 Complete elliptic integrals

5.111

1. 

K(k)k2p+3dk=1(2p+3)2{ 4(p+1)2K(k)k2p+1dk+k2p+2[ E(k)(2p+3)K(k)k2 ] }

si2_e  BY (610.04)

2. 

E(k)k2p+3dk=14p2+16p+15{4(p+1)2E(k)k2p+1dkE(k)k2p+2[(2p+3)k22]k2p+2k2K(k)}

si3_e  BY (611.04)

5.112

1. 

K(k)dk=πk2[ 1+j=1[ (2j)! ]2k2j(2j+1)24j(j!)4 ]

  BY (610.00)

2.6 

E(k)dk=πk2[ 1j=1[ (

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