Fungrim symbol: BesselKDerivative

Symbol: BesselKDerivative —

K^{(r)}_{\nu}\!\left(z\right)

— Differentiated modified Bessel function of the second kind

The following table lists all conditions such that BesselKDerivative(nu, z, r) is defined in Fungrim.

Domain	Codomain
Numbers
$\nu \in \mathbb{R} \,\mathbin{\operatorname{and}}\, z \in \left(0, \infty\right) \,\mathbin{\operatorname{and}}\, r \in \mathbb{Z}_{\ge 0}$	$K^{(r)}_{\nu}\!\left(z\right) \in \mathbb{R}$
$\nu \in \mathbb{C} \setminus \left\{0\right\} \,\mathbin{\operatorname{and}}\, z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, r \in \mathbb{Z}_{\ge 0}$	$K^{(r)}_{\nu}\!\left(z\right) \in \mathbb{C}$

Table data:

\left(P, Q\right)

such that

\left(P\right) \implies \left(Q\right)

Definitions:

Fungrim symbol	Notation	Short description
`BesselKDerivative`	$K^{(r)}_{\nu}\!\left(z\right)$	Differentiated modified Bessel function of the second kind
`RR`	$\mathbb{R}$	Real numbers
`OpenInterval`	$\left(a, b\right)$	Open interval
`Infinity`	$\infty$	Positive infinity
`ZZGreaterEqual`	$\mathbb{Z}_{\ge n}$	Integers greater than or equal to n
`CC`	$\mathbb{C}$	Complex numbers

Source code for this entry:

Entry(ID("ddfb97"),
    SymbolDefinition(BesselKDerivative, BesselKDerivative(nu, z, r), "Differentiated modified Bessel function of the second kind"),
    Description("The following table lists all conditions such that", SourceForm(BesselKDerivative(nu, z, r)), "is defined in Fungrim."),
    Table(TableRelation(Tuple(P, Q), Implies(P, Q)), TableHeadings(Description("Domain"), Description("Codomain")), List(TableSection("Numbers"), Tuple(And(Element(nu, RR), Element(z, OpenInterval(0, Infinity)), Element(r, ZZGreaterEqual(0))), Element(BesselKDerivative(nu, z, r), RR)), Tuple(And(Element(nu, SetMinus(CC, Set(0))), Element(z, CC), Element(r, ZZGreaterEqual(0))), Element(BesselKDerivative(nu, z, r), CC)))))

Topics using this symbol

The symbol BesselKDerivative appears in 2 topics:

Recurrence relations for Bessel functions (in 4 entries)
Bessel functions (in 3 entries)

Entries using this symbol

The symbol BesselKDerivative appears in 6 entries: