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Fungrim entry: 5bb42e

Symbol: BesselY Yν ⁣(z)Y_{\nu}\!\left(z\right) Bessel function of the second kind
The following table lists all conditions such that BesselY(nu, z) is defined in Fungrim.
Domain Codomain
Numbers
νRandz(0,)\nu \in \mathbb{R} \,\mathbin{\operatorname{and}}\, z \in \left(0, \infty\right) Yν ⁣(z)RY_{\nu}\!\left(z\right) \in \mathbb{R}
νC{0}andzC\nu \in \mathbb{C} \setminus \left\{0\right\} \,\mathbin{\operatorname{and}}\, z \in \mathbb{C} Yν ⁣(z)CY_{\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
BesselYYν ⁣(z)Y_{\nu}\!\left(z\right) Bessel function of the second kind
RRR\mathbb{R} Real numbers
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("5bb42e"),
    SymbolDefinition(BesselY, BesselY(nu, z), "Bessel function of the second kind"),
    Description("The following table lists all conditions such that", SourceForm(BesselY(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, RR), Element(z, OpenInterval(0, Infinity))), Element(BesselY(nu, z), RR)), Tuple(And(Element(nu, SetMinus(CC, Set(0))), Element(z, CC)), Element(BesselY(nu, z), CC)))))

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

2019-06-18 07:49:59.356594 UTC