Fungrim symbol: BesselK

Symbol: BesselK —

K_{\nu}\!\left(z\right)

— Modified Bessel function of the second kind

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

Domain	Codomain
Numbers
$\nu \in \mathbb{R} \,\mathbin{\operatorname{and}}\, z \in \left(0, \infty\right)$	$K_{\nu}\!\left(z\right) \in \mathbb{R}$
$\nu \in \mathbb{C} \setminus \left\{0\right\} \,\mathbin{\operatorname{and}}\, z \in \mathbb{C}$	$K_{\nu}\!\left(z\right) \in \mathbb{C}$

Table data:

\left(P, Q\right)

such that

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

Definitions:

Fungrim symbol	Notation	Short description
`BesselK`	$K_{\nu}\!\left(z\right)$	Modified Bessel function of the second kind
`RR`	$\mathbb{R}$	Real numbers
`OpenInterval`	$\left(a, b\right)$	Open interval
`Infinity`	$\infty$	Positive infinity
`CC`	$\mathbb{C}$	Complex numbers

Source code for this entry:

Entry(ID("ff93d0"),
    SymbolDefinition(BesselK, BesselK(nu, z), "Modified Bessel function of the second kind"),
    Description("The following table lists all conditions such that", SourceForm(BesselK(nu, z)), "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(BesselK(nu, z), RR)), Tuple(And(Element(nu, SetMinus(CC, Set(0))), Element(z, CC)), Element(BesselK(nu, z), CC)))))

Topics using this symbol

The symbol BesselK appears in 4 topics:

Bessel functions (in 8 entries)
Specific values of Bessel functions (in 6 entries)
Recurrence relations for Bessel functions (in 4 entries)
Hypergeometric representations of Bessel functions (in 2 entries)

Entries using this symbol

The symbol BesselK appears in 16 entries: