Fungrim entry: 8236ff

\left(x \in \left[0, \infty\right) \;\mathbin{\operatorname{and}}\; y \in \left[0, \infty\right) \;\mathbin{\operatorname{and}}\; z \in \left(0, \infty\right) \;\mathbin{\operatorname{and}}\; \left(x \ne 0 \;\mathbin{\operatorname{or}}\; y \ne 0\right)\right) \;\implies\; R_D\!\left(x, y, z\right) \in \left(0, \infty\right)

TeX:

\left(x \in \left[0, \infty\right) \;\mathbin{\operatorname{and}}\; y \in \left[0, \infty\right) \;\mathbin{\operatorname{and}}\; z \in \left(0, \infty\right) \;\mathbin{\operatorname{and}}\; \left(x \ne 0 \;\mathbin{\operatorname{or}}\; y \ne 0\right)\right) \;\implies\; R_D\!\left(x, y, z\right) \in \left(0, \infty\right)

Definitions:

Fungrim symbol	Notation	Short description
`ClosedOpenInterval`	$\left[a, b\right)$	Closed-open interval
`Infinity`	$\infty$	Positive infinity
`OpenInterval`	$\left(a, b\right)$	Open interval
`CarlsonRD`	$R_D\!\left(x, y, z\right)$	Degenerate Carlson symmetric elliptic integral of the third kind

Source code for this entry:

Entry(ID("8236ff"),
    Formula(Implies(And(Element(x, ClosedOpenInterval(0, Infinity)), Element(y, ClosedOpenInterval(0, Infinity)), Element(z, OpenInterval(0, Infinity)), Or(NotEqual(x, 0), NotEqual(y, 0))), Element(CarlsonRD(x, y, z), OpenInterval(0, Infinity)))),
    Variables(x, y, z))

Topics using this entry

Carlson symmetric elliptic integrals