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Fungrim entry: 522c1a

Symbol: BesselIDerivative Iν(r) ⁣(z)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
νZandzRandrZ0\nu \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, z \in \mathbb{R} \,\mathbin{\operatorname{and}}\, r \in \mathbb{Z}_{\ge 0} Iν(r) ⁣(z)RI^{(r)}_{\nu}\!\left(z\right) \in \mathbb{R}
νRandz(0,)andrZ0\nu \in \mathbb{R} \,\mathbin{\operatorname{and}}\, z \in \left(0, \infty\right) \,\mathbin{\operatorname{and}}\, r \in \mathbb{Z}_{\ge 0} Iν(r) ⁣(z)RI^{(r)}_{\nu}\!\left(z\right) \in \mathbb{R}
νZandzCandrZ0\nu \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, r \in \mathbb{Z}_{\ge 0} Iν(r) ⁣(z)CI^{(r)}_{\nu}\!\left(z\right) \in \mathbb{C}
νCandzC{0}andrZ0\nu \in \mathbb{C} \,\mathbin{\operatorname{and}}\, z \in \mathbb{C} \setminus \left\{0\right\} \,\mathbin{\operatorname{and}}\, r \in \mathbb{Z}_{\ge 0} Iν(r) ⁣(z)CI^{(r)}_{\nu}\!\left(z\right) \in \mathbb{C}
Table data: (P,Q)\left(P, Q\right) such that (P)    (Q)\left(P\right) \implies \left(Q\right)
Definitions:
Fungrim symbol Notation Short description
BesselIDerivativeIν(r) ⁣(z)I^{(r)}_{\nu}\!\left(z\right) Differentiated modified Bessel function of the first kind
ZZZ\mathbb{Z} Integers
RRR\mathbb{R} Real numbers
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
OpenInterval(a,b)\left(a, b\right) Open interval
Infinity\infty Positive infinity
CCC\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)))))

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

2019-08-17 11:32:46.829430 UTC