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
`BesselJDerivative`	$J^{(r)}_{\nu}\!\left(z\right)$	Differentiated 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), BesselJDerivative(n, 0, Add(r, 2))), Mul(Mul(Add(r, 1), Add(r, 2)), BesselJDerivative(n, 0, r))), 0)),
    Variables(nu, r),
    Assumptions(And(Element(n, ZZ), Element(r, ZZGreaterEqual(0)))))

Topics using this entry

Recurrence relations for Bessel functions