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# Fungrim entry: 15ac84

$\left({r}^{2} + 4 r - {n}^{2} + 4\right) J^{(r + 2)}_{n}\!\left(0\right) + \left(r + 1\right) \left(r + 2\right) J^{(r)}_{n}\!\left(0\right) = 0$
Assumptions:$n \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; r \in \mathbb{Z}_{\ge 0}$
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
Pow${a}^{b}$ Power
BesselJ$J_{\nu}\!\left(z\right)$ Bessel function of the first kind
ZZ$\mathbb{Z}$ Integers
ZZGreaterEqual$\mathbb{Z}_{\ge n}$ 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(n, r),
Assumptions(And(Element(n, ZZ), Element(r, ZZGreaterEqual(0)))))

## Topics using this entry

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

2021-03-15 19:12:00.328586 UTC