Overload List
| # | Signature | Description |
|---|---|---|
| 1 | void EllipJacoby(double u, double m, double Epsilon, double &sn, double &cn, double &dn); | Jacobi elliptic functions sn, cn and dn. |
| 2 | void EllipJacoby(float u, float m, float Epsilon, float &sn, float &cn, float &dn); |
Overload 1: void EllipJacoby(double u, double m, double Epsilon, double &sn, double &cn, double &dn);
Jacobi elliptic functions sn, cn and dn.
| # | Name | Type | Description |
|---|---|---|---|
| 1 | u | double | Defines value at which the functions will be evaluated (any real). |
| 2 | m | double | Defines the parameter m = k^2, a real value on the closed interval [0,1]. |
| 3 | Epsilon | double | Defines the accuracy for the AGM/Landen iteration. |
| 4 | sn | double & | Returns Jacobi elliptic function sn(u,m). |
| 5 | cn | double & | Returns Jacobi elliptic function cn(u,m). |
| 6 | dn | double & | Returns Jacobi elliptic function dn(u,m). |
Computes the three Jacobi elliptic functions sn(u,m), cn(u,m) and dn(u,m) at argument u with parameter m = k^2 (modulus squared), using the descending Landen / AGM transformation to accuracy Epsilon. They are the inverse of the incomplete elliptic integral of the first kind: if u=\int_0^{\varphi} d\theta/\sqrt{1-m\sin^2\theta} then
sn(u,m)=sinvarphi, cn(u,m)=cosvarphi, dn(u,m)=sqrt(1-m sn^2(u,m)).
They satisfy the identities sn^2+cn^2=1 and dn^2+m\,sn^2=1. Degenerate limits handled exactly: at m=0, (sn,cn,dn)=(\sin u,\cos u,1); at m=1, (sn,cn,dn)=(\tanh u,\operatorname{sech} u,\operatorname{sech} u). Domain: u any real value; the parameter m on the closed interval [0,1]. For m<0 or m>1 an exception is raised.
Overload 2: void EllipJacoby(float u, float m, float Epsilon, float &sn, float &cn, float &dn);
| # | Name | Type | Description |
|---|---|---|---|
| 1 | u | float | |
| 2 | m | float | |
| 3 | Epsilon | float | |
| 4 | sn | float & | |
| 5 | cn | float & | |
| 6 | dn | float & |