Fungrim entry: d5b7e8

Y_{n}\!\left(z\right) = -\frac{2}{\pi} \left({i}^{n} K_{n}\!\left(i z\right) + \left(\log\!\left(i z\right) - \log\!\left(z\right)\right) J_{n}\!\left(z\right)\right)

Assumptions:

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

TeX:

Y_{n}\!\left(z\right) = -\frac{2}{\pi} \left({i}^{n} K_{n}\!\left(i z\right) + \left(\log\!\left(i z\right) - \log\!\left(z\right)\right) J_{n}\!\left(z\right)\right)

n \in \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...)
`Pow`	${a}^{b}$	Power
`ConstI`	$i$	Imaginary unit
`BesselK`	$K_{\nu}\!\left(z\right)$	Modified Bessel function of the second kind
`Log`	$\log\!\left(z\right)$	Natural logarithm
`BesselJ`	$J_{\nu}\!\left(z\right)$	Bessel function of the first kind
`ZZ`	$\mathbb{Z}$	Integers
`CC`	$\mathbb{C}$	Complex numbers

Source code for this entry:

Entry(ID("d5b7e8"),
    Formula(Equal(BesselY(n, z), Mul(Neg(Div(2, ConstPi)), Add(Mul(Pow(ConstI, n), BesselK(n, Mul(ConstI, z))), Mul(Sub(Log(Mul(ConstI, z)), Log(z)), BesselJ(n, z)))))),
    Variables(n, z),
    Assumptions(And(Element(n, ZZ), Element(z, SetMinus(CC, Set(0))))))

Topics using this entry

Bessel functions