Fungrim home page

Fungrim entry: e1a3cb

RJ ⁣(0,0,z,w)={sgn ⁣(1zw),z0  and  w0~,otherwiseR_J\!\left(0, 0, z, w\right) = \begin{cases} \operatorname{sgn}\!\left(\frac{1}{\sqrt{z} w}\right) \infty, & z \ne 0 \;\mathbin{\operatorname{and}}\; w \ne 0\\{\tilde \infty}, & \text{otherwise}\\ \end{cases}
Assumptions:zC  and  wCz \in \mathbb{C} \;\mathbin{\operatorname{and}}\; w \in \mathbb{C}
R_J\!\left(0, 0, z, w\right) = \begin{cases} \operatorname{sgn}\!\left(\frac{1}{\sqrt{z} w}\right) \infty, & z \ne 0 \;\mathbin{\operatorname{and}}\; w \ne 0\\{\tilde \infty}, & \text{otherwise}\\ \end{cases}

z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; w \in \mathbb{C}
Fungrim symbol Notation Short description
CarlsonRJRJ ⁣(x,y,z,w)R_J\!\left(x, y, z, w\right) Carlson symmetric elliptic integral of the third kind
Signsgn(z)\operatorname{sgn}(z) Sign function
Sqrtz\sqrt{z} Principal square root
Infinity\infty Positive infinity
UnsignedInfinity~{\tilde \infty} Unsigned infinity
CCC\mathbb{C} Complex numbers
Source code for this entry:
    Formula(Equal(CarlsonRJ(0, 0, z, w), Cases(Tuple(Mul(Sign(Div(1, Mul(Sqrt(z), w))), Infinity), And(NotEqual(z, 0), NotEqual(w, 0))), Tuple(UnsignedInfinity, Otherwise)))),
    Variables(z, w),
    Assumptions(And(Element(z, CC), Element(w, CC))))

Topics using this entry

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2021-03-15 19:12:00.328586 UTC