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Fungrim entry: 65647f

I3/2 ⁣(z)=(2zπ)1/2(cosh⁡ ⁣(z)z−sinh⁡ ⁣(z)z2)I_{3 / 2}\!\left(z\right) = {\left(\frac{2 z}{\pi}\right)}^{1 / 2} \left(\frac{\cosh\!\left(z\right)}{z} - \frac{\sinh\!\left(z\right)}{{z}^{2}}\right)
Assumptions:z∈C∖{0}z \in \mathbb{C} \setminus \left\{0\right\}
TeX:
I_{3 / 2}\!\left(z\right) = {\left(\frac{2 z}{\pi}\right)}^{1 / 2} \left(\frac{\cosh\!\left(z\right)}{z} - \frac{\sinh\!\left(z\right)}{{z}^{2}}\right)

z \in \mathbb{C} \setminus \left\{0\right\}
Definitions:
Fungrim symbol Notation Short description
BesselIIν ⁣(z)I_{\nu}\!\left(z\right) Modified Bessel function of the first kind
Powab{a}^{b} Power
ConstPiπ\pi The constant pi (3.14...)
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("65647f"),
    Formula(Equal(BesselI(Div(3, 2), z), Mul(Pow(Div(Mul(2, z), ConstPi), Div(1, 2)), Sub(Div(Cosh(z), z), Div(Sinh(z), Pow(z, 2)))))),
    Variables(z),
    Assumptions(Element(z, SetMinus(CC, Set(0)))))

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2019-06-18 07:49:59.356594 UTC