# Fungrim entry: 49d754

$K_{1 / 3}\!\left(z\right) = \frac{\sqrt{3} \pi}{\omega} \operatorname{Ai}\!\left({\omega}^{2}\right)\; \text{ where } \omega = {\left(\frac{3 z}{2}\right)}^{1 / 3}$
Assumptions:$z \in \mathbb{C} \setminus \left\{0\right\}$
TeX:
K_{1 / 3}\!\left(z\right) = \frac{\sqrt{3} \pi}{\omega} \operatorname{Ai}\!\left({\omega}^{2}\right)\; \text{ where } \omega = {\left(\frac{3 z}{2}\right)}^{1 / 3}

z \in \mathbb{C} \setminus \left\{0\right\}
Definitions:
Fungrim symbol Notation Short description
BesselK$K_{\nu}\!\left(z\right)$ Modified Bessel function of the second kind
Sqrt$\sqrt{z}$ Principal square root
Pi$\pi$ The constant pi (3.14...)
AiryAi$\operatorname{Ai}\!\left(z\right)$ Airy function of the first kind
Pow${a}^{b}$ Power
CC$\mathbb{C}$ Complex numbers
Source code for this entry:
Entry(ID("49d754"),
Formula(Equal(BesselK(Div(1, 3), z), Where(Mul(Div(Mul(Sqrt(3), Pi), omega), AiryAi(Pow(omega, 2))), Equal(omega, Pow(Div(Mul(3, z), 2), Div(1, 3)))))),
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.

2020-01-31 18:09:28.494564 UTC