Fungrim entry: c362e8

K_{2 / 3}\!\left(z\right) = -\frac{\sqrt{3} \pi}{{\omega}^{2}} \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_{2 / 3}\!\left(z\right) = -\frac{\sqrt{3} \pi}{{\omega}^{2}} \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...)
`Pow`	${a}^{b}$	Power
`CC`	$\mathbb{C}$	Complex numbers

Source code for this entry:

Entry(ID("c362e8"),
    Formula(Equal(BesselK(Div(2, 3), z), Where(Neg(Mul(Div(Mul(Sqrt(3), ConstPi), Pow(omega, 2)), AiryAiPrime(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