Fungrim entry: 5679f2

Y_{-1 / 2}\!\left(z\right) = {\left(\frac{2 z}{\pi}\right)}^{1 / 2} \frac{\sin(z)}{z}

Assumptions:

z \in \mathbb{C} \setminus \left\{0\right\}

TeX:

Y_{-1 / 2}\!\left(z\right) = {\left(\frac{2 z}{\pi}\right)}^{1 / 2} \frac{\sin(z)}{z}

z \in \mathbb{C} \setminus \left\{0\right\}

Definitions:

Fungrim symbol	Notation	Short description
`BesselY`	$Y_{\nu}\!\left(z\right)$	Bessel function of the second kind
`Pow`	${a}^{b}$	Power
`Pi`	$\pi$	The constant pi (3.14...)
`Sin`	$\sin(z)$	Sine
`CC`	$\mathbb{C}$	Complex numbers

Source code for this entry:

Entry(ID("5679f2"),
    Formula(Equal(BesselY(Neg(Div(1, 2)), z), Mul(Pow(Div(Mul(2, z), Pi), Div(1, 2)), Div(Sin(z), z)))),
    Variables(z),
    Assumptions(Element(z, SetMinus(CC, Set(0)))))

Topics using this entry

Specific values of Bessel functions

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