Fungrim entry: 2a4195

Y_{\nu}\!\left(z\right) = \frac{\cos\!\left(\pi \nu\right) J_{\nu}\!\left(z\right) - J_{-\nu}\!\left(z\right)}{\sin\!\left(\pi \nu\right)}

Assumptions:

\nu \in \mathbb{C} \setminus \mathbb{Z} \,\mathbin{\operatorname{and}}\, z \in \mathbb{C} \setminus \left\{0\right\}

TeX:

Y_{\nu}\!\left(z\right) = \frac{\cos\!\left(\pi \nu\right) J_{\nu}\!\left(z\right) - J_{-\nu}\!\left(z\right)}{\sin\!\left(\pi \nu\right)}

\nu \in \mathbb{C} \setminus \mathbb{Z} \,\mathbin{\operatorname{and}}\, 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
`ConstPi`	$\pi$	The constant pi (3.14...)
`BesselJ`	$J_{\nu}\!\left(z\right)$	Bessel function of the first kind
`Sin`	$\sin\!\left(z\right)$	Sine
`CC`	$\mathbb{C}$	Complex numbers
`ZZ`	$\mathbb{Z}$	Integers

Source code for this entry:

Entry(ID("2a4195"),
    Formula(Equal(BesselY(nu, z), Div(Sub(Mul(Cos(Mul(ConstPi, nu)), BesselJ(nu, z)), BesselJ(Neg(nu), z)), Sin(Mul(ConstPi, nu))))),
    Variables(nu, z),
    Assumptions(And(Element(nu, SetMinus(CC, ZZ)), Element(z, SetMinus(CC, Set(0))))))

Topics using this entry

Bessel functions