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Fungrim entry: e7b5be

Jν ⁣(x)0.6749ν1/3\left|J_{\nu}\!\left(x\right)\right| \le 0.6749 {\nu}^{-1 / 3}
Assumptions:ν(0,)andx[0,)\nu \in \left(0, \infty\right) \,\mathbin{\operatorname{and}}\, x \in \left[0, \infty\right)
References:
  • L. Landau. Monotonicity and bounds on Bessel functions. Proceedings of the Symposium on Mathematical Physics and Quantum Field Theory. Vol. 4. Southwest Texas State Univ. San Marcos, TX, 2000. http://emis.ams.org/journals/EJDE/conf-proc/04/l1/landau.pdf
TeX:
\left|J_{\nu}\!\left(x\right)\right| \le 0.6749 {\nu}^{-1 / 3}

\nu \in \left(0, \infty\right) \,\mathbin{\operatorname{and}}\, x \in \left[0, \infty\right)
Definitions:
Fungrim symbol Notation Short description
Absz\left|z\right| Absolute value
BesselJJν ⁣(z)J_{\nu}\!\left(z\right) Bessel function of the first kind
Powab{a}^{b} Power
OpenInterval(a,b)\left(a, b\right) Open interval
Infinity\infty Positive infinity
ClosedOpenInterval[a,b)\left[a, b\right) Closed-open interval
Source code for this entry:
Entry(ID("e7b5be"),
    Formula(LessEqual(Abs(BesselJ(nu, x)), Mul(Decimal("0.6749"), Pow(nu, Neg(Div(1, 3)))))),
    Variables(nu, x),
    Assumptions(And(Element(nu, OpenInterval(0, Infinity)), Element(x, ClosedOpenInterval(0, Infinity)))),
    References("L. Landau. Monotonicity and bounds on Bessel functions. Proceedings of the Symposium on Mathematical Physics and Quantum Field Theory. Vol. 4. Southwest Texas State Univ. San Marcos, TX, 2000. http://emis.ams.org/journals/EJDE/conf-proc/04/l1/landau.pdf"))

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

2019-09-19 20:12:49.583742 UTC