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Fungrim entry: ddfb97

Symbol: BesselKDerivative Kν(r) ⁣(z)K^{(r)}_{\nu}\!\left(z\right) Differentiated modified Bessel function of the second kind
The following table lists all conditions such that BesselKDerivative(nu, z, r) is defined in Fungrim.
Domain Codomain
Numbers
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} Kν(r) ⁣(z)RK^{(r)}_{\nu}\!\left(z\right) \in \mathbb{R}
νC{0}andzCandrZ0\nu \in \mathbb{C} \setminus \left\{0\right\} \,\mathbin{\operatorname{and}}\, z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, r \in \mathbb{Z}_{\ge 0} Kν(r) ⁣(z)CK^{(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
BesselKDerivativeKν(r) ⁣(z)K^{(r)}_{\nu}\!\left(z\right) Differentiated modified Bessel function of the second kind
RRR\mathbb{R} Real numbers
OpenInterval(a,b)\left(a, b\right) Open interval
Infinity\infty Positive infinity
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("ddfb97"),
    SymbolDefinition(BesselKDerivative, BesselKDerivative(nu, z, r), "Differentiated modified Bessel function of the second kind"),
    Description("The following table lists all conditions such that", SourceForm(BesselKDerivative(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, RR), Element(z, OpenInterval(0, Infinity)), Element(r, ZZGreaterEqual(0))), Element(BesselKDerivative(nu, z, r), RR)), Tuple(And(Element(nu, SetMinus(CC, Set(0))), Element(z, CC), Element(r, ZZGreaterEqual(0))), Element(BesselKDerivative(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.

2019-08-17 11:32:46.829430 UTC