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Fungrim entry: d5b7e8

Yn ⁣(z)=2π(inKn ⁣(iz)+(log ⁣(iz)log(z))Jn ⁣(z))Y_{n}\!\left(z\right) = -\frac{2}{\pi} \left({i}^{n} K_{n}\!\left(i z\right) + \left(\log\!\left(i z\right) - \log(z)\right) J_{n}\!\left(z\right)\right)
Assumptions:nZ  and  zC{0}n \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C} \setminus \left\{0\right\}
Y_{n}\!\left(z\right) = -\frac{2}{\pi} \left({i}^{n} K_{n}\!\left(i z\right) + \left(\log\!\left(i z\right) - \log(z)\right) J_{n}\!\left(z\right)\right)

n \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C} \setminus \left\{0\right\}
Fungrim symbol Notation Short description
BesselYYν ⁣(z)Y_{\nu}\!\left(z\right) Bessel function of the second kind
Piπ\pi The constant pi (3.14...)
Powab{a}^{b} Power
ConstIii Imaginary unit
BesselKKν ⁣(z)K_{\nu}\!\left(z\right) Modified Bessel function of the second kind
Loglog(z)\log(z) Natural logarithm
BesselJJν ⁣(z)J_{\nu}\!\left(z\right) Bessel function of the first kind
ZZZ\mathbb{Z} Integers
CCC\mathbb{C} Complex numbers
Source code for this entry:
    Formula(Equal(BesselY(n, z), Mul(Neg(Div(2, Pi)), 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))))))

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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