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Fungrim entry: 351d87

sinc(x)<2xtanh ⁣(x2)\left|\operatorname{sinc}(x)\right| < \frac{\sqrt{2}}{x} \tanh\!\left(\frac{x}{\sqrt{2}}\right)
Assumptions:xR  and  x0x \in \mathbb{R} \;\mathbin{\operatorname{and}}\; x \ne 0
TeX:
\left|\operatorname{sinc}(x)\right| < \frac{\sqrt{2}}{x} \tanh\!\left(\frac{x}{\sqrt{2}}\right)

x \in \mathbb{R} \;\mathbin{\operatorname{and}}\; x \ne 0
Definitions:
Fungrim symbol Notation Short description
Absz\left|z\right| Absolute value
Sincsinc(z)\operatorname{sinc}(z) Sinc function
Sqrtz\sqrt{z} Principal square root
RRR\mathbb{R} Real numbers
Source code for this entry:
Entry(ID("351d87"),
    Formula(Less(Abs(Sinc(x)), Mul(Div(Sqrt(2), x), Tanh(Div(x, Sqrt(2)))))),
    Variables(x),
    Assumptions(And(Element(x, RR), NotEqual(x, 0))))

Topics using this entry

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

2020-08-27 09:56:25.682319 UTC