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Fungrim entry: 0836b4

∣Jn ⁣(z)∣≤exp⁡ ⁣(∣Im⁡ ⁣(z)∣)\left|J_{n}\!\left(z\right)\right| \le \exp\!\left(\left|\operatorname{Im}\!\left(z\right)\right|\right)
Assumptions:n∈Z and⁡ z∈Cn \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, z \in \mathbb{C}
TeX:
\left|J_{n}\!\left(z\right)\right| \le \exp\!\left(\left|\operatorname{Im}\!\left(z\right)\right|\right)

n \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, z \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
Abs∣z∣\left|z\right| Absolute value
BesselJJν ⁣(z)J_{\nu}\!\left(z\right) Bessel function of the first kind
Expez{e}^{z} Exponential function
ImIm⁡ ⁣(z)\operatorname{Im}\!\left(z\right) Imaginary part
ZZZ\mathbb{Z} Integers
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("0836b4"),
    Formula(LessEqual(Abs(BesselJ(n, z)), Exp(Abs(Im(z))))),
    Variables(n, z),
    Assumptions(And(Element(n, ZZ), Element(z, CC))))

Topics using this entry

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

2019-06-18 07:49:59.356594 UTC