ellipticIntegralE¶
Evaluates the complete elliptic integral of the second kind E(x).
Synopsis¶
ellipticIntegralE (x)
Required Arguments¶
- float
x
(Input) - Argument for which the function value is desired.
Return Value¶
The complete elliptic integral E(x).
Description¶
The complete elliptic integral of the second kind is defined to be
\[E(x) = \int_0^{\pi/2} \left[1 - x \sin^2 \theta\right]^{1/2} d \theta
\text{ for } 0 \leq x < 1\]
The argument x must satisfy 0 ≤ x < 1; otherwise, ellipticIntegralE
returns machine(2), the largest representable floating-point number. For
more information, see the description for machine.
The function E(x) is computed using the routine ellipticIntegralRF and ellipticIntegralRD. The computation is done using the relation
\[E(x) = R_F(0,1-x,1) - \tfrac{x}{3} R_D(0,1-x,1)\]