Fungrim entry: 538c8c

R_F\!\left(0, x, c x\right) = \frac{K\!\left(1 - c\right)}{\sqrt{x}}

Assumptions:

x \in \mathbb{C} \;\mathbin{\operatorname{and}}\; c \in \left[0, \infty\right)

TeX:

R_F\!\left(0, x, c x\right) = \frac{K\!\left(1 - c\right)}{\sqrt{x}}

x \in \mathbb{C} \;\mathbin{\operatorname{and}}\; c \in \left[0, \infty\right)

Definitions:

Fungrim symbol	Notation	Short description
`CarlsonRF`	$R_F\!\left(x, y, z\right)$	Carlson symmetric elliptic integral of the first kind
`EllipticK`	$K(m)$	Legendre complete elliptic integral of the first kind
`Sqrt`	$\sqrt{z}$	Principal square root
`CC`	$\mathbb{C}$	Complex numbers
`ClosedOpenInterval`	$\left[a, b\right)$	Closed-open interval
`Infinity`	$\infty$	Positive infinity

Source code for this entry:

Entry(ID("538c8c"),
    Formula(Equal(CarlsonRF(0, x, Mul(c, x)), Div(EllipticK(Sub(1, c)), Sqrt(x)))),
    Variables(x, c),
    Assumptions(And(Element(x, CC), Element(c, ClosedOpenInterval(0, Infinity)))))

Topics using this entry

Specific values of Carlson symmetric elliptic integrals