Fungrim home page

Fungrim entry: 40aeb6

Yν′ ⁣(z)=Yν−1 ⁣(z)−Yν+1 ⁣(z)2Y'_{\nu}\!\left(z\right) = \frac{Y_{\nu - 1}\!\left(z\right) - Y_{\nu + 1}\!\left(z\right)}{2}
Assumptions:ν∈C  and⁡  z∈C∖{0}\nu \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C} \setminus \left\{0\right\}
TeX:
Y'_{\nu}\!\left(z\right) = \frac{Y_{\nu - 1}\!\left(z\right) - Y_{\nu + 1}\!\left(z\right)}{2}

\nu \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C} \setminus \left\{0\right\}
Definitions:
Fungrim symbol Notation Short description
BesselYYν ⁣(z)Y_{\nu}\!\left(z\right) Bessel function of the second kind
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("40aeb6"),
    Formula(Equal(BesselY(nu, z, 1), Div(Sub(BesselY(Sub(nu, 1), z), BesselY(Add(nu, 1), z)), 2))),
    Variables(nu, z),
    Assumptions(And(Element(nu, CC), 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