Fungrim entry: a0ff0b

K'_{\nu}\!\left(z\right) = -\frac{K_{\nu - 1}\!\left(z\right) + K_{\nu + 1}\!\left(z\right)}{2}

Assumptions:

\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
`BesselKDerivative`	$K^{(r)}_{\nu}\!\left(z\right)$	Differentiated modified Bessel function of the second kind
`BesselK`	$K_{\nu}\!\left(z\right)$	Modified Bessel function of the second kind
`CC`	$\mathbb{C}$	Complex numbers

Source code for this entry:

Entry(ID("a0ff0b"),
    Formula(Equal(BesselKDerivative(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))))))

Topics using this entry

Bessel functions
Recurrence relations for Bessel functions