Fungrim entry: cc4cd8

\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(\left(x \ne 0 \;\mathbin{\operatorname{and}}\; y \ne 0\right) \;\mathbin{\operatorname{or}}\; \left(x \ne 0 \;\mathbin{\operatorname{and}}\; z \ne 0\right) \;\mathbin{\operatorname{or}}\; \left(y \ne 0 \;\mathbin{\operatorname{and}}\; z \ne 0\right)\right)\right) \;\implies\; R_F\!\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(\left(x \ne 0 \;\mathbin{\operatorname{and}}\; y \ne 0\right) \;\mathbin{\operatorname{or}}\; \left(x \ne 0 \;\mathbin{\operatorname{and}}\; z \ne 0\right) \;\mathbin{\operatorname{or}}\; \left(y \ne 0 \;\mathbin{\operatorname{and}}\; z \ne 0\right)\right)\right) \;\implies\; R_F\!\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
`CarlsonRF`	$R_F\!\left(x, y, z\right)$	Carlson symmetric elliptic integral of the first kind
`OpenInterval`	$\left(a, b\right)$	Open interval

Source code for this entry:

Entry(ID("cc4cd8"),
    Formula(Implies(And(Element(x, ClosedOpenInterval(0, Infinity)), Element(y, ClosedOpenInterval(0, Infinity)), Element(z, ClosedOpenInterval(0, Infinity)), Or(And(NotEqual(x, 0), NotEqual(y, 0)), And(NotEqual(x, 0), NotEqual(z, 0)), And(NotEqual(y, 0), NotEqual(z, 0)))), Element(CarlsonRF(x, y, z), OpenInterval(0, Infinity)))),
    Variables(x, y, z))

Topics using this entry

Carlson symmetric elliptic integrals