Assumptions:
TeX:
R_D\!\left(0, y, z\right) = {y}^{-3 / 2} \begin{cases} \frac{3 \left(E\!\left(1 - \frac{z}{y}\right) - \frac{z}{y} K\!\left(1 - \frac{z}{y}\right)\right)}{\frac{z}{y} \left(1 - \frac{z}{y}\right)}, & z \ne 0 \;\mathbin{\operatorname{and}}\; z \ne y\\\frac{3 \pi}{4}, & z = y\\{\tilde \infty}, & z = 0\\ \end{cases}
y \in \mathbb{C} \setminus \left\{0\right\} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; \left|\arg(y) - \arg(z)\right| < \piDefinitions:
| Fungrim symbol | Notation | Short description |
|---|---|---|
| CarlsonRD | Degenerate Carlson symmetric elliptic integral of the third kind | |
| Pow | Power | |
| EllipticE | Legendre complete elliptic integral of the second kind | |
| EllipticK | Legendre complete elliptic integral of the first kind | |
| Pi | The constant pi (3.14...) | |
| UnsignedInfinity | Unsigned infinity | |
| CC | Complex numbers | |
| Abs | Absolute value | |
| Arg | Complex argument |
Source code for this entry:
Entry(ID("4e4380"),
Formula(Equal(CarlsonRD(0, y, z), Mul(Pow(y, Neg(Div(3, 2))), Cases(Tuple(Div(Mul(3, Sub(EllipticE(Sub(1, Div(z, y))), Mul(Div(z, y), EllipticK(Sub(1, Div(z, y)))))), Mul(Div(z, y), Sub(1, Div(z, y)))), And(NotEqual(z, 0), NotEqual(z, y))), Tuple(Div(Mul(3, Pi), 4), Equal(z, y)), Tuple(UnsignedInfinity, Equal(z, 0)))))),
Variables(y, z),
Assumptions(And(Element(y, SetMinus(CC, Set(0))), Element(z, CC), Less(Abs(Sub(Arg(y), Arg(z))), Pi))))