Fungrim symbol: BesselJDerivative

Symbol: BesselJDerivative —

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

— Differentiated Bessel function of the first kind

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

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

Table data:

\left(P, Q\right)

such that

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

Definitions:

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

Source code for this entry:

Entry(ID("0fea28"),
    SymbolDefinition(BesselJDerivative, BesselJDerivative(nu, z, r), "Differentiated Bessel function of the first kind"),
    Description("The following table lists all conditions such that", SourceForm(BesselJDerivative(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, ZZ), Element(z, RR), Element(r, ZZGreaterEqual(0))), Element(BesselJDerivative(nu, z, r), RR)), Tuple(And(Element(nu, RR), Element(z, OpenInterval(0, Infinity)), Element(r, ZZGreaterEqual(0))), Element(BesselJDerivative(nu, z, r), RR)), Tuple(And(Element(nu, ZZ), Element(z, CC), Element(r, ZZGreaterEqual(0))), Element(BesselJDerivative(nu, z, r), CC)), Tuple(And(Element(nu, CC), Element(z, SetMinus(CC, Set(0))), Element(r, ZZGreaterEqual(0))), Element(BesselJDerivative(nu, z, r), CC)))))

Topics using this symbol

The symbol BesselJDerivative appears in 2 topics:

Recurrence relations for Bessel functions (in 5 entries)
Bessel functions (in 3 entries)

Entries using this symbol

The symbol BesselJDerivative appears in 7 entries: