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[ (

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