Fungrim home page

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(z)}{z} - \frac{\sinh(z)}{{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(z)}{z} - \frac{\sinh(z)}{{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
Piπ\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), Pi), Div(1, 2)), Sub(Div(Cosh(z), z), Div(Sinh(z), Pow(z, 2)))))),
    Variables(z),
    Assumptions(Element(z, SetMinus(CC, Set(0)))))

Topics using this entry

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2021-03-15 19:12:00.328586 UTC