# Fungrim entry: e7b5be

$\left|J_{\nu}\!\left(x\right)\right| \le 0.6749 {\nu}^{-1 / 3}$
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 0.6749 {\nu}^{-1 / 3}

\nu \in \left(0, \infty\right) \,\mathbin{\operatorname{and}}\, x \in \left[0, \infty\right)
Definitions:
Fungrim symbol Notation Short description
Abs$\left|z\right|$ Absolute value
BesselJ$J_{\nu}\!\left(z\right)$ Bessel function of the first kind
Pow${a}^{b}$ Power
OpenInterval$\left(a, b\right)$ Open interval
Infinity$\infty$ Positive infinity
ClosedOpenInterval$\left[a, b\right)$ 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"))

## Topics using this entry

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

2020-01-31 18:09:28.494564 UTC