# Fungrim entry: c28288

$E\!\left(\phi + k \pi, m\right) = E\!\left(\phi, m\right) + 2 k E(m)$
Assumptions:$\phi \in \mathbb{C} \;\mathbin{\operatorname{and}}\; m \in \mathbb{C} \;\mathbin{\operatorname{and}}\; k \in \mathbb{Z}$
TeX:
E\!\left(\phi + k \pi, m\right) = E\!\left(\phi, m\right) + 2 k E(m)

\phi \in \mathbb{C} \;\mathbin{\operatorname{and}}\; m \in \mathbb{C} \;\mathbin{\operatorname{and}}\; k \in \mathbb{Z}
Definitions:
Fungrim symbol Notation Short description
IncompleteEllipticE$E\!\left(\phi, m\right)$ Legendre incomplete elliptic integral of the second kind
Pi$\pi$ The constant pi (3.14...)
EllipticE$E(m)$ Legendre complete elliptic integral of the second kind
CC$\mathbb{C}$ Complex numbers
ZZ$\mathbb{Z}$ Integers
Source code for this entry:
Entry(ID("c28288"),