Campus Livre
ellipticF
Incomplete elliptic integral of the first kind.
Category: Mathematics > Mathematical Functions
Syntax
F = ellipticF(phi, m)Evaluates the integral from 0 to phi of 1/sqrt(1 - m*sin(t)^2).
Description
With phi = pi/2 it reduces to the complete integral ellipticK(m). It is the inverse of the Jacobi amplitude: if u = ellipticF(phi, m) then phi = jacobiAM(u, m). The time a pendulum needs to reach a given angle is given by this function.
Input arguments
phi- Amplitude angle in radians.
m- Parameter (
m = k^2).
Output arguments
F- Array of the same size after broadcasting the inputs.
Example
Incomplete and complete cases
ellipticF(pi/4, 0.5)
ellipticF(pi/2, 0.5)
ellipticK(0.5)Output
ans = 0.8260
ans = 1.8541
ans = 1.8541