Elliptic integral of the second kind
ellipticE (<ϕ>, m)
ellipticE(m) represents the complete elliptic integral of the second kind which is defined as
ellipticE( φ ,m) represents the incomplete elliptic integral of the second kind which is defined as
The elliptic integrals of the second kind are defined for complex arguments ϕ and m.
A floating-point value is computed if all arguments are numerical and at least one is a floating-point value. Unevaluated symbolic calls are returned for most exact arguments. For some special cases explicit symbolic representations are returned.
When called with floating-point arguments, this function is sensitive to the environment variable DIGITS which determines the numerical working precision.
Most calls with exact arguments return themselves unevaluated:
ellipticK(1/2); ellipticF(PI/4, I);
Some special arguments return explicit symbolic representations:
ellipticF(PI/2, 1/2); ellipticF(1, 1);
If one argument is a floating-point value and the others can be converted to a floating-point values, then a floating-point result will be returned:
ellipticPi(0.5, PI/3, 1);
An arithmetical expression specifying the parameter.
An arithmetical expression specifying the amplitude. In case of ellipticE and ellipticPi, the default is .