Fungrim entry: 3e05c6

R_D\!\left(0, y, 1\right) = \begin{cases} \frac{3 \left(K\!\left(1 - y\right) - E\!\left(1 - y\right)\right)}{1 - y}, & y \ne 1\\\frac{3 \pi}{4}, & y = 1\\ \end{cases}

Assumptions:

y \in \mathbb{C}

TeX:

R_D\!\left(0, y, 1\right) = \begin{cases} \frac{3 \left(K\!\left(1 - y\right) - E\!\left(1 - y\right)\right)}{1 - y}, & y \ne 1\\\frac{3 \pi}{4}, & y = 1\\ \end{cases}

y \in \mathbb{C}

Definitions:

Fungrim symbol	Notation	Short description
`CarlsonRD`	$R_D\!\left(x, y, z\right)$	Degenerate Carlson symmetric elliptic integral of the third kind
`EllipticK`	$K(m)$	Legendre complete elliptic integral of the first kind
`EllipticE`	$E(m)$	Legendre complete elliptic integral of the second kind
`Pi`	$\pi$	The constant pi (3.14...)
`CC`	$\mathbb{C}$	Complex numbers

Source code for this entry:

Entry(ID("3e05c6"),
    Formula(Equal(CarlsonRD(0, y, 1), Cases(Tuple(Div(Mul(3, Sub(EllipticK(Sub(1, y)), EllipticE(Sub(1, y)))), Sub(1, y)), NotEqual(y, 1)), Tuple(Div(Mul(3, Pi), 4), Equal(y, 1))))),
    Variables(y),
    Assumptions(Element(y, CC)))

Topics using this entry

Specific values of Carlson symmetric elliptic integrals