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Fungrim entry: 2a4195

Yν ⁣(z)=cos ⁣(πν)Jν ⁣(z)Jν ⁣(z)sin ⁣(πν)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:νCZandzC{0}\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
BesselYYν ⁣(z)Y_{\nu}\!\left(z\right) Bessel function of the second kind
ConstPiπ\pi The constant pi (3.14...)
BesselJJν ⁣(z)J_{\nu}\!\left(z\right) Bessel function of the first kind
Sinsin(z)\sin(z) Sine
CCC\mathbb{C} Complex numbers
ZZZ\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))))))

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Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2019-10-05 13:11:19.856591 UTC