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Fungrim entry: c362e8

K2/3 ⁣(z)=3πω2Ai ⁣(ω2)   where ω=(3z2)1/3K_{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:zC{0}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
BesselKKν ⁣(z)K_{\nu}\!\left(z\right) Modified Bessel function of the second kind
Sqrtz\sqrt{z} Principal square root
ConstPiπ\pi The constant pi (3.14...)
Powab{a}^{b} Power
AiryAiAi ⁣(z)\operatorname{Ai}\!\left(z\right) Airy function of the first kind
CCC\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)), AiryAi(Pow(omega, 2), 1))), Equal(omega, Pow(Div(Mul(3, z), 2), Div(1, 3)))))),
    Variables(z),
    Assumptions(Element(z, SetMinus(CC, Set(0)))))

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2019-09-22 15:43:45.410764 UTC