Fungrim home page

Fungrim entry: 8236ff

(x[0,)  and  y[0,)  and  z(0,)  and  (x0  or  y0))        RD ⁣(x,y,z)(0,)\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)
\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)
Fungrim symbol Notation Short description
ClosedOpenInterval[a,b)\left[a, b\right) Closed-open interval
Infinity\infty Positive infinity
OpenInterval(a,b)\left(a, b\right) Open interval
CarlsonRDRD ⁣(x,y,z)R_D\!\left(x, y, z\right) Degenerate Carlson symmetric elliptic integral of the third kind
Source code for this entry:
    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

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