Overload List
| # | Signature | Description |
|---|---|---|
| 1 | Double EllipComplete(Double m) | Complete elliptic integral of the first kind, K(m). |
| 2 | Double EllipComplete(Double m, Double Epsilon, ref Double e) | Complete elliptic integrals of the first and second kind, K(m) and E(m). |
| 3 | Single EllipComplete(Single m) | |
| 4 | Single EllipComplete(Single m, Single Epsilon, ref Single e) |
Overload 1: Double EllipComplete(Double m)
Complete elliptic integral of the first kind, K(m).
| # | Name | Description |
|---|---|---|
| 1 | m | Defines the integral parameter m = k^2, a real value on the closed interval [0,1]. |
Returns: Double - the complete elliptic integral of the first kind K(m), evaluated at the parameter m. Parameter m must lie on the closed interval [0,1], otherwise an exception is raised.
Computes the complete elliptic integral of the first kind in the parameter convention m = k^2 (m is the modulus squared, not the
modulus k), evaluated by the arithmetic-geometric-mean (AGM) iteration:
K(m)=integral _0^(pi/2)dtheta/(sqrt(1-m sin^2theta))=pi/(2 AGM(1,sqrt(1-m))).
Domain: the parameter m must lie on the closed interval [0,1]. Boundary behavior: K(0)=\pi/2; at m=1 the integral diverges and the routine returns +INF. For m<0 or m>1 the argument is outside the domain and an exception is raised (it does not return NaN).
Overload 2: Double EllipComplete(Double m, Double Epsilon, ref Double e)
Complete elliptic integrals of the first and second kind, K(m) and E(m).
| # | Name | Description |
|---|---|---|
| 1 | m | Defines the integral parameter m = k^2, a real value on the closed interval [0,1]. |
| 2 | Epsilon | Defines the accuracy for the AGM iteration used to evaluate both elliptic integrals. |
| 3 | e | Returns the value of the complete elliptic integral of the second kind E(m), evaluated at the parameter m, to the accuracy Epsilon. |
Returns: Double - the complete elliptic integral of the first kind K(m), evaluated at the parameter m. Parameter m must lie on the closed interval [0,1], otherwise an exception is raised.
Returns the complete elliptic integral of the first kind K(m) and, through the out-parameter e, the complete elliptic integral of the second kind E(m), both in the parameter convention m = k^2, computed by a shared AGM iteration to accuracy Epsilon:
K(m)=integral _0^(pi/2)dtheta/(sqrt(1-m sin^2theta)), E(m)=integral _0^(pi/2)sqrt(1-m sin^2theta) dtheta.
Domain: m on the closed interval [0,1]. Boundary behavior: K(0)=E(0)=\pi/2; at m=1, K=+INF and E=1. For m<0 or m>1 an exception is raised (no NaN return).
Overload 3: Single EllipComplete(Single m)
| # | Name | Type | Description |
|---|---|---|---|
| 1 | m | Single | scalar |
Returns: Single
Overload 4: Single EllipComplete(Single m, Single Epsilon, ref Single e)
| # | Name | Type | Description |
|---|---|---|---|
| 1 | m | Single | scalar |
| 2 | Epsilon | Single | scalar |
| 3 | e | Single (ref) |
Returns: Single