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Fungrim entry: 99c0b3

zcz2=z1cz\sqrt{z - c {z}^{2}} = \sqrt{z} \sqrt{1 - c z}
Assumptions:zCandc[0,)z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, c \in \left[0, \infty\right)
TeX:
\sqrt{z - c {z}^{2}} = \sqrt{z} \sqrt{1 - c z}

z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, c \in \left[0, \infty\right)
Definitions:
Fungrim symbol Notation Short description
Sqrtz\sqrt{z} Principal square root
Powab{a}^{b} Power
CCC\mathbb{C} Complex numbers
ClosedOpenInterval[a,b)\left[a, b\right) Closed-open interval
Infinity\infty Positive infinity
Source code for this entry:
Entry(ID("99c0b3"),
    Formula(Equal(Sqrt(Sub(z, Mul(c, Pow(z, 2)))), Mul(Sqrt(z), Sqrt(Sub(1, Mul(c, z)))))),
    Variables(z, c),
    Assumptions(And(Element(z, CC), Element(c, ClosedOpenInterval(0, Infinity)))))

Topics using this entry

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

2019-08-21 11:44:15.926409 UTC