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Fungrim entry: 15ac84

(r2+4rn2+4)Jn(r+2) ⁣(0)+(r+1)(r+2)Jn(r) ⁣(0)=0\left({r}^{2} + 4 r - {n}^{2} + 4\right) J^{(r + 2)}_{n}\!\left(0\right) + \left(r + 1\right) \left(r + 2\right) J^{(r)}_{n}\!\left(0\right) = 0
Assumptions:nZandrZ0n \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, r \in \mathbb{Z}_{\ge 0}
TeX:
\left({r}^{2} + 4 r - {n}^{2} + 4\right) J^{(r + 2)}_{n}\!\left(0\right) + \left(r + 1\right) \left(r + 2\right) J^{(r)}_{n}\!\left(0\right) = 0

n \in \mathbb{Z} \,\mathbin{\operatorname{and}}\, r \in \mathbb{Z}_{\ge 0}
Definitions:
Fungrim symbol Notation Short description
Powab{a}^{b} Power
BesselJJν ⁣(z)J_{\nu}\!\left(z\right) Bessel function of the first kind
ZZZ\mathbb{Z} Integers
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
Entry(ID("15ac84"),
    Formula(Equal(Add(Mul(Add(Sub(Add(Pow(r, 2), Mul(4, r)), Pow(n, 2)), 4), BesselJ(n, 0, Add(r, 2))), Mul(Mul(Add(r, 1), Add(r, 2)), BesselJ(n, 0, r))), 0)),
    Variables(nu, r),
    Assumptions(And(Element(n, ZZ), Element(r, ZZGreaterEqual(0)))))

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

2019-10-05 13:11:19.856591 UTC