`ellipticCE`

Complementary complete elliptic integral of the second kind.

Category: Mathematics > Mathematical Functions

Syntax

E1 = ellipticCE(m)

Returns E(1 - m), the complete integral ellipticE at the complementary parameter.

Description

The complementary integral is E'(m) = E(1 - m), the arc-length integral of an ellipse seen with the roles of the axes swapped. It appears in Legendre's relation E*K' + E'*K - K*K' = pi/2.

Input arguments

m: Parameter, 0 <= m <= 1 for real results (the square of the modulus k).

Output arguments

E1: Array of the same size as m.

Example

Complement of E

m = 0.3;
ellipticCE(m)
ellipticE(1 - m)

Output

ans = 1.2417
ans = 1.2417

See also

ellipticE ellipticCK ellipticK ellipke