Fungrim entry: 3e1435

\frac{d}{d x}\, R_G\!\left(x, y, z\right) + \frac{d}{d y}\, R_G\!\left(x, y, z\right) + \frac{d}{d z}\, R_G\!\left(x, y, z\right) = \frac{1}{2} R_F\!\left(x, y, z\right)

Assumptions:

x \in \mathbb{C} \setminus \left(-\infty, 0\right] \;\mathbin{\operatorname{and}}\; y \in \mathbb{C} \setminus \left(-\infty, 0\right] \;\mathbin{\operatorname{and}}\; z \in \mathbb{C} \setminus \left(-\infty, 0\right]

TeX:

x \in \mathbb{C} \setminus \left(-\infty, 0\right] \;\mathbin{\operatorname{and}}\; y \in \mathbb{C} \setminus \left(-\infty, 0\right] \;\mathbin{\operatorname{and}}\; z \in \mathbb{C} \setminus \left(-\infty, 0\right]

Definitions:

Fungrim symbol	Notation	Short description
`ComplexDerivative`	$\frac{d}{d z}\, f\!\left(z\right)$	Complex derivative
`CarlsonRG`	$R_G\!\left(x, y, z\right)$	Carlson symmetric elliptic integral of the second kind
`CarlsonRF`	$R_F\!\left(x, y, z\right)$	Carlson symmetric elliptic integral of the first kind
`CC`	$\mathbb{C}$	Complex numbers
`OpenClosedInterval`	$\left(a, b\right]$	Open-closed interval
`Infinity`	$\infty$	Positive infinity

Source code for this entry:

Entry(ID("3e1435"),
    Equal(Add(Add(ComplexDerivative(CarlsonRG(x, y, z), For(x, x)), ComplexDerivative(CarlsonRG(x, y, z), For(y, y))), ComplexDerivative(CarlsonRG(x, y, z), For(z, z))), Mul(Div(1, 2), CarlsonRF(x, y, z))),
    Variables(x, y, z),
    Assumptions(And(Element(x, SetMinus(CC, OpenClosedInterval(Neg(Infinity), 0))), Element(y, SetMinus(CC, OpenClosedInterval(Neg(Infinity), 0))), Element(z, SetMinus(CC, OpenClosedInterval(Neg(Infinity), 0))))))

Topics using this entry

Carlson symmetric elliptic integrals