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Fungrim entry: a0ff0b

Kν ⁣(z)=Kν1 ⁣(z)+Kν+1 ⁣(z)2K'_{\nu}\!\left(z\right) = -\frac{K_{\nu - 1}\!\left(z\right) + K_{\nu + 1}\!\left(z\right)}{2}
Assumptions:νCandzC{0}\nu \in \mathbb{C} \,\mathbin{\operatorname{and}}\, z \in \mathbb{C} \setminus \left\{0\right\}
TeX:
K'_{\nu}\!\left(z\right) = -\frac{K_{\nu - 1}\!\left(z\right) + K_{\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
BesselKKν ⁣(z)K_{\nu}\!\left(z\right) Modified Bessel function of the second kind
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("a0ff0b"),
    Formula(Equal(BesselK(nu, z, 1), Neg(Div(Add(BesselK(Sub(nu, 1), z), BesselK(Add(nu, 1), z)), 2)))),
    Variables(nu, z),
    Assumptions(And(Element(nu, CC), 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.

2019-09-15 11:00:55.020619 UTC