Fungrim entry: 8ac81d

Symbol: BesselI —

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

— Modified Bessel function of the first kind

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

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

Table data:

\left(P, Q\right)

such that

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

Definitions:

Fungrim symbol	Notation	Short description
`BesselI`	$I_{\nu}\!\left(z\right)$	Modified Bessel function of the first kind
`ZZ`	$\mathbb{Z}$	Integers
`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("8ac81d"),
    SymbolDefinition(BesselI, BesselI(nu, z), "Modified Bessel function of the first kind"),
    Description("The following table lists all conditions such that", SourceForm(BesselI(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, ZZ), Element(z, RR)), Element(BesselI(nu, z), RR)), Tuple(And(Element(nu, RR), Element(z, OpenInterval(0, Infinity))), Element(BesselI(nu, z), RR)), Tuple(And(Element(nu, ZZ), Element(z, CC)), Element(BesselI(nu, z), CC)), Tuple(And(Element(nu, CC), Element(z, SetMinus(CC, Set(0)))), Element(BesselI(nu, z), CC)))))

Topics using this entry

Bessel functions