Fungrim entry: 40aeb6

Y'_{\nu}\!\left(z\right) = \frac{Y_{\nu - 1}\!\left(z\right) - Y_{\nu + 1}\!\left(z\right)}{2}

Assumptions:

\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
`BesselYDerivative`	$Y^{(r)}_{\nu}\!\left(z\right)$	Differentiated Bessel function of the second kind
`BesselY`	$Y_{\nu}\!\left(z\right)$	Bessel function of the second kind
`CC`	$\mathbb{C}$	Complex numbers

Source code for this entry:

Entry(ID("40aeb6"),
    Formula(Equal(BesselYDerivative(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

Bessel functions
Recurrence relations for Bessel functions