Fungrim home page

Fungrim entry: 0fea28

Symbol: BesselJDerivative Jν(r) ⁣(z)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
νZandzRandrZ0\nu \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, z \in \mathbb{R} \,\mathbin{\operatorname{and}}\, r \in \mathbb{Z}_{\ge 0} Jν(r) ⁣(z)RJ^{(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} Jν(r) ⁣(z)RJ^{(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} Jν(r) ⁣(z)CJ^{(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} Jν(r) ⁣(z)CJ^{(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
BesselJDerivativeJν(r) ⁣(z)J^{(r)}_{\nu}\!\left(z\right) Differentiated 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("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 entry

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

2019-08-19 14:38:23.809000 UTC