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Fungrim entry: 5d16e5

sinc(n)(x)1\left|{\operatorname{sinc}}^{(n)}(x)\right| \le 1
Assumptions:xR  and  nZ0x \in \mathbb{R} \;\mathbin{\operatorname{and}}\; n \in \mathbb{Z}_{\ge 0}
\left|{\operatorname{sinc}}^{(n)}(x)\right| \le 1

x \in \mathbb{R} \;\mathbin{\operatorname{and}}\; n \in \mathbb{Z}_{\ge 0}
Fungrim symbol Notation Short description
Absz\left|z\right| Absolute value
Derivativeddzf ⁣(z)\frac{d}{d z}\, f\!\left(z\right) Derivative
Sincsinc(z)\operatorname{sinc}(z) Sinc function
RRR\mathbb{R} Real numbers
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
    Formula(LessEqual(Abs(Derivative(Sinc(x), For(x, x, n))), 1)),
    Variables(x, n),
    Assumptions(And(Element(x, RR), Element(n, ZZGreaterEqual(0)))))

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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