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Fungrim entry: 7f3485

Jν ⁣(x)0.7858x1/3\left|J_{\nu}\!\left(x\right)\right| \le 0.7858 {x}^{-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 0.7858 {x}^{-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
ClosedOpenInterval[a,b)\left[a, b\right) Closed-open interval
Infinity\infty Positive infinity
OpenInterval(a,b)\left(a, b\right) Open interval
Source code for this entry:
Entry(ID("7f3485"),
    Formula(LessEqual(Abs(BesselJ(nu, x)), Mul(Decimal("0.7858"), Pow(x, Neg(Div(1, 3)))))),
    Variables(nu, x),
    Assumptions(And(Element(nu, ClosedOpenInterval(0, Infinity)), Element(x, OpenInterval(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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2019-09-20 18:07:53.062439 UTC