Fungrim entry: 9d98f8

$K_{\nu}\!\left(z\right) = -\frac{z}{2 \nu} \left(K_{\nu - 1}\!\left(z\right) - K_{\nu + 1}\!\left(z\right)\right)$
Assumptions:$\nu \in \mathbb{Z} \setminus \left\{0\right\} \,\mathbin{\operatorname{and}}\, z \in \mathbb{C}$
Alternative assumptions:$\nu \in \mathbb{C} \setminus \left\{0\right\} \,\mathbin{\operatorname{and}}\, z \in \mathbb{C} \setminus \left\{0\right\}$
TeX:
K_{\nu}\!\left(z\right) = -\frac{z}{2 \nu} \left(K_{\nu - 1}\!\left(z\right) - K_{\nu + 1}\!\left(z\right)\right)

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

\nu \in \mathbb{C} \setminus \left\{0\right\} \,\mathbin{\operatorname{and}}\, z \in \mathbb{C} \setminus \left\{0\right\}
Definitions:
Fungrim symbol Notation Short description
BesselK$K_{\nu}\!\left(z\right)$ Modified Bessel function of the second kind
ZZ$\mathbb{Z}$ Integers
CC$\mathbb{C}$ Complex numbers
Source code for this entry:
Entry(ID("9d98f8"),
Formula(Equal(BesselK(nu, z), Neg(Mul(Div(z, Mul(2, nu)), Sub(BesselK(Sub(nu, 1), z), BesselK(Add(nu, 1), z)))))),
Variables(nu, z),
Assumptions(And(Element(nu, SetMinus(ZZ, Set(0))), Element(z, CC)), And(Element(nu, SetMinus(CC, Set(0))), Element(z, SetMinus(CC, Set(0))))))

Topics using this entry

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

2019-12-30 15:00:46.909060 UTC