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))))))

Fungrim entry: 9d98f8

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