Fungrim entry: 4091ad

R_G\!\left(-x, -y, z\right) = -\overline{i R_G\!\left(x, y, -z\right)}

Assumptions:

x \in \left[0, \infty\right) \;\mathbin{\operatorname{and}}\; y \in \left[0, \infty\right) \;\mathbin{\operatorname{and}}\; z \in \left[0, \infty\right)

TeX:

R_G\!\left(-x, -y, z\right) = -\overline{i R_G\!\left(x, y, -z\right)}

x \in \left[0, \infty\right) \;\mathbin{\operatorname{and}}\; y \in \left[0, \infty\right) \;\mathbin{\operatorname{and}}\; z \in \left[0, \infty\right)

Definitions:

Fungrim symbol	Notation	Short description
`CarlsonRG`	$R_G\!\left(x, y, z\right)$	Carlson symmetric elliptic integral of the second kind
`Conjugate`	$\overline{z}$	Complex conjugate
`ConstI`	$i$	Imaginary unit
`ClosedOpenInterval`	$\left[a, b\right)$	Closed-open interval
`Infinity`	$\infty$	Positive infinity

Source code for this entry:

Entry(ID("4091ad"),
    Formula(Equal(CarlsonRG(Neg(x), Neg(y), z), Neg(Conjugate(Mul(ConstI, CarlsonRG(x, y, Neg(z))))))),
    Variables(x, y, z),
    Assumptions(And(Element(x, ClosedOpenInterval(0, Infinity)), Element(y, ClosedOpenInterval(0, Infinity)), Element(z, ClosedOpenInterval(0, Infinity)))))

Topics using this entry

Specific values of Carlson symmetric elliptic integrals