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Fungrim entry: 3bffa9

Jν ⁣(x)1\left|J_{\nu}\!\left(x\right)\right| \le 1
Assumptions:ν[0,)  and  xR\nu \in \left[0, \infty\right) \;\mathbin{\operatorname{and}}\; x \in \mathbb{R}
\left|J_{\nu}\!\left(x\right)\right| \le 1

\nu \in \left[0, \infty\right) \;\mathbin{\operatorname{and}}\; x \in \mathbb{R}
Fungrim symbol Notation Short description
Absz\left|z\right| Absolute value
BesselJJν ⁣(z)J_{\nu}\!\left(z\right) Bessel function of the first kind
ClosedOpenInterval[a,b)\left[a, b\right) Closed-open interval
Infinity\infty Positive infinity
RRR\mathbb{R} Real numbers
Source code for this entry:
    Formula(LessEqual(Abs(BesselJ(nu, x)), 1)),
    Variables(nu, x),
    Assumptions(And(Element(nu, ClosedOpenInterval(0, Infinity)), Element(x, RR))))

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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