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Fungrim entry: 0c09cc

K3/2 ⁣(z)=(πz2)1/2e−z(1z+1z2)K_{3 / 2}\!\left(z\right) = {\left(\frac{\pi z}{2}\right)}^{1 / 2} {e}^{-z} \left(\frac{1}{z} + \frac{1}{{z}^{2}}\right)
Assumptions:z∈C∖{0}z \in \mathbb{C} \setminus \left\{0\right\}
TeX:
K_{3 / 2}\!\left(z\right) = {\left(\frac{\pi z}{2}\right)}^{1 / 2} {e}^{-z} \left(\frac{1}{z} + \frac{1}{{z}^{2}}\right)

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
Piπ\pi The constant pi (3.14...)
Expez{e}^{z} Exponential function
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("0c09cc"),
    Formula(Equal(BesselK(Div(3, 2), z), Mul(Pow(Div(Mul(Pi, z), 2), Div(1, 2)), Mul(Exp(Neg(z)), Add(Div(1, z), Div(1, Pow(z, 2))))))),
    Variables(z),
    Assumptions(Element(z, SetMinus(CC, Set(0)))))

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2021-03-15 19:12:00.328586 UTC