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
`ConstPi`	$\pi$	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), ConstPi), 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

Specific values of Bessel functions