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Fungrim entry: d1f5c5

K1/2 ⁣(z)=(πz2)1/2e−zzK_{1 / 2}\!\left(z\right) = {\left(\frac{\pi z}{2}\right)}^{1 / 2} \frac{{e}^{-z}}{z}
Assumptions:z∈C∖{0}z \in \mathbb{C} \setminus \left\{0\right\}
TeX:
K_{1 / 2}\!\left(z\right) = {\left(\frac{\pi z}{2}\right)}^{1 / 2} \frac{{e}^{-z}}{z}

z \in \mathbb{C} \setminus \left\{0\right\}
Definitions:
Fungrim symbol Notation Short description
BesselKKν ⁣(z)K_{\nu}\!\left(z\right) Modified Bessel function of the second kind
Powab{a}^{b} Power
ConstPiπ\pi The constant pi (3.14...)
Expez{e}^{z} Exponential function
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("d1f5c5"),
    Formula(Equal(BesselK(Div(1, 2), z), Mul(Pow(Div(Mul(ConstPi, z), 2), Div(1, 2)), Div(Exp(Neg(z)), z)))),
    Variables(z),
    Assumptions(Element(z, SetMinus(CC, Set(0)))))

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