# Fungrim entry: 522c1a

Symbol: BesselIDerivative $I^{(r)}_{\nu}\!\left(z\right)$ Differentiated modified Bessel function of the first kind
The following table lists all conditions such that BesselIDerivative(nu, z, r) is defined in Fungrim.
Domain Codomain
Numbers
$\nu \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, z \in \mathbb{R} \,\mathbin{\operatorname{and}}\, r \in \mathbb{Z}_{\ge 0}$ $I^{(r)}_{\nu}\!\left(z\right) \in \mathbb{R}$
$\nu \in \mathbb{R} \,\mathbin{\operatorname{and}}\, z \in \left(0, \infty\right) \,\mathbin{\operatorname{and}}\, r \in \mathbb{Z}_{\ge 0}$ $I^{(r)}_{\nu}\!\left(z\right) \in \mathbb{R}$
$\nu \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, r \in \mathbb{Z}_{\ge 0}$ $I^{(r)}_{\nu}\!\left(z\right) \in \mathbb{C}$
$\nu \in \mathbb{C} \,\mathbin{\operatorname{and}}\, z \in \mathbb{C} \setminus \left\{0\right\} \,\mathbin{\operatorname{and}}\, r \in \mathbb{Z}_{\ge 0}$ $I^{(r)}_{\nu}\!\left(z\right) \in \mathbb{C}$
Table data: $\left(P, Q\right)$ such that $\left(P\right) \implies \left(Q\right)$
Definitions:
Fungrim symbol Notation Short description
BesselIDerivative$I^{(r)}_{\nu}\!\left(z\right)$ Differentiated modified 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("522c1a"),
SymbolDefinition(BesselIDerivative, BesselIDerivative(nu, z, r), "Differentiated modified Bessel function of the first kind"),
Description("The following table lists all conditions such that", SourceForm(BesselIDerivative(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(BesselIDerivative(nu, z, r), RR)), Tuple(And(Element(nu, RR), Element(z, OpenInterval(0, Infinity)), Element(r, ZZGreaterEqual(0))), Element(BesselIDerivative(nu, z, r), RR)), Tuple(And(Element(nu, ZZ), Element(z, CC), Element(r, ZZGreaterEqual(0))), Element(BesselIDerivative(nu, z, r), CC)), Tuple(And(Element(nu, CC), Element(z, SetMinus(CC, Set(0))), Element(r, ZZGreaterEqual(0))), Element(BesselIDerivative(nu, z, r), CC)))))

## Topics using this entry

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2019-09-08 12:55:28.957599 UTC