Fungrim entry: 7f3485

\left|J_{\nu}\!\left(x\right)\right| \le 0.7858 {x}^{-1 / 3}

Assumptions:

\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
`Abs`	$\left\|z\right\|$	Absolute value
`BesselJ`	$J_{\nu}\!\left(z\right)$	Bessel function of the first kind
`Pow`	${a}^{b}$	Power
`ClosedOpenInterval`	$\left[a, b\right)$	Closed-open interval
`Infinity`	$\infty$	Positive infinity
`OpenInterval`	$\left(a, b\right)$	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"))

Topics using this entry

Bessel functions