Fungrim entry: afabeb

F\!\left(\frac{\pi k}{2}, m\right) = k K(m)

Assumptions:

m \in \mathbb{C} \;\mathbin{\operatorname{and}}\; k \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; \left(k \ne 0 \;\mathbin{\operatorname{or}}\; m \ne 1\right)

TeX:

F\!\left(\frac{\pi k}{2}, m\right) = k K(m)

m \in \mathbb{C} \;\mathbin{\operatorname{and}}\; k \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; \left(k \ne 0 \;\mathbin{\operatorname{or}}\; m \ne 1\right)

Definitions:

Fungrim symbol	Notation	Short description
`IncompleteEllipticF`	$F\!\left(\phi, m\right)$	Legendre incomplete elliptic integral of the first kind
`Pi`	$\pi$	The constant pi (3.14...)
`EllipticK`	$K(m)$	Legendre complete elliptic integral of the first kind
`CC`	$\mathbb{C}$	Complex numbers
`ZZ`	$\mathbb{Z}$	Integers

Source code for this entry:

Entry(ID("afabeb"),
    Formula(Equal(IncompleteEllipticF(Div(Mul(Pi, k), 2), m), Mul(k, EllipticK(m)))),
    Variables(m, k),
    Assumptions(And(Element(m, CC), Element(k, ZZ), Or(NotEqual(k, 0), NotEqual(m, 1)))))

Topics using this entry

Legendre elliptic integrals