Assumptions:
Alternative assumptions:
TeX:
{z}^{2} \left({r}^{2} + 7 r + 12\right) \frac{J^{(r + 4)}_{\nu}\!\left(z\right)}{\left(r + 4\right)!} + z \left(2 {r}^{2} + 11 r + 15\right) \frac{J^{(r + 3)}_{\nu}\!\left(z\right)}{\left(r + 3\right)!} + \left(r \left(r + 4\right) + {z}^{2} - {\nu}^{2} + 4\right) \frac{J^{(r + 2)}_{\nu}\!\left(z\right)}{\left(r + 2\right)!} + 2 z \frac{J^{(r + 1)}_{\nu}\!\left(z\right)}{\left(r + 1\right)!} + \frac{J^{(r)}_{\nu}\!\left(z\right)}{r !} = 0
\nu \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; r \in \mathbb{Z}_{\ge 0}
\nu \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C} \setminus \left\{0\right\} \;\mathbin{\operatorname{and}}\; r \in \mathbb{Z}_{\ge 0}Definitions:
| Fungrim symbol | Notation | Short description |
|---|---|---|
| Pow | Power | |
| BesselJ | Bessel function of the first kind | |
| Factorial | Factorial | |
| ZZ | Integers | |
| CC | Complex numbers | |
| ZZGreaterEqual | Integers greater than or equal to n |
Source code for this entry:
Entry(ID("9b2f38"),
Formula(Equal(Add(Add(Add(Add(Mul(Mul(Pow(z, 2), Add(Add(Pow(r, 2), Mul(7, r)), 12)), Div(BesselJ(nu, z, Add(r, 4)), Factorial(Add(r, 4)))), Mul(Mul(z, Add(Add(Mul(2, Pow(r, 2)), Mul(11, r)), 15)), Div(BesselJ(nu, z, Add(r, 3)), Factorial(Add(r, 3))))), Mul(Add(Sub(Add(Mul(r, Add(r, 4)), Pow(z, 2)), Pow(nu, 2)), 4), Div(BesselJ(nu, z, Add(r, 2)), Factorial(Add(r, 2))))), Mul(Mul(2, z), Div(BesselJ(nu, z, Add(r, 1)), Factorial(Add(r, 1))))), Div(BesselJ(nu, z, r), Factorial(r))), 0)),
Variables(nu, z, r),
Assumptions(And(Element(nu, ZZ), Element(z, CC), Element(r, ZZGreaterEqual(0))), And(Element(nu, CC), Element(z, SetMinus(CC, Set(0))), Element(r, ZZGreaterEqual(0)))))