Campus Livre
jacobiZeta
Jacobi zeta function Z(u|m).
Category: Mathematics > Mathematical Functions
Syntax
Z = jacobiZeta(u, m)Evaluates the Jacobi zeta function at u for parameter m.
Description
The Jacobi zeta function is Z(u|m) = E(phi|m) - (E(m)/K(m))*F(phi|m), where phi is the amplitude of u, E(phi|m) and F(phi|m) are the incomplete elliptic integrals of the second and first kinds, and K(m), E(m) are the complete ones. It measures how far the incomplete integral of the second kind departs from a straight line.
It is periodic in u with period 2*K(m) and equals zero at u = 0. For m = 0 it is identically zero.
Input arguments
u- Argument, numeric or symbolic.
m- Parameter,
m = k^2.
Output arguments
Z- Values of the Jacobi zeta function, with the size of the inputs.
Example
Evaluate and check the trivial case
jacobiZeta(0.5, 0.3)
jacobiZeta(0.5, 0)Output
ans = 0.0666
ans = 0