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"),
    Formula(Equal(IncompleteEllipticE(Add(phi, Mul(k, Pi)), m), Add(IncompleteEllipticE(phi, m), Mul(Mul(2, k), EllipticE(m))))),
    Variables(phi, m, k),
    Assumptions(And(Element(phi, CC), Element(m, CC), Element(k, ZZ))))

Topics using this entry

Legendre elliptic integrals