About the Project
NIST

general elliptic functions

AdvancedHelp

(0.007 seconds)

1—10 of 91 matching pages

1: 19.2 Definitions
§19.2(i) General Elliptic Integrals
is called an elliptic integral. …
§19.2(ii) Legendre’s Integrals
§19.2(iii) Bulirsch’s Integrals
§19.2(iv) A Related Function: R C ( x , y )
2: 21.8 Abelian Functions
In consequence, Abelian functions are generalizations of elliptic functions23.2(iii)) to more than one complex variable. …
3: 23.2 Definitions and Periodic Properties
23.2.9 ( z + 2 ω j ) = ( z ) , j = 1 , 2 , 3 .
4: 23.6 Relations to Other Functions
§23.6(iii) General Elliptic Functions
For representations of general elliptic functions23.2(iii)) in terms of σ ( z ) and ( z ) see Lawden (1989, §§8.9, 8.10), and for expansions in terms of ζ ( z ) see Lawden (1989, §8.11). …
5: 22.7 Landen Transformations
§22.7(iii) Generalized Landen Transformations
6: 22.2 Definitions
22.2.10 p q ( z , k ) = p r ( z , k ) q r ( z , k ) = 1 q p ( z , k ) ,
22.2.11 p q ( z , k ) = θ p ( z | τ ) / θ q ( z | τ ) ,
7: 22.17 Moduli Outside the Interval [0,1]
22.17.1 p q ( z , k ) = p q ( z , - k ) ,
8: 22.6 Elementary Identities
22.6.22 p q 2 ( 1 2 z , k ) = p s ( z , k ) + r s ( z , k ) q s ( z , k ) + r s ( z , k ) = p q ( z , k ) + r q ( z , k ) 1 + r q ( z , k ) = p r ( z , k ) + 1 q r ( z , k ) + 1 .
9: 19.25 Relations to Other Functions
19.25.28 Δ ( p , q ) = p s 2 ( u , k ) - q s 2 ( u , k ) = - Δ ( q , p ) ,
19.25.31 u = R F ( p s 2 ( u , k ) , q s 2 ( u , k ) , r s 2 ( u , k ) ) ;
10: 22.14 Integrals
22.14.2 cn ( x , k ) d x = k - 1 Arccos ( dn ( x , k ) ) ,
22.14.5 sd ( x , k ) d x = ( k k ) - 1 Arcsin ( - k cd ( x , k ) ) ,