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Fungrim entry: 7377c8

z2(r2+7r+12)Kν(r+4) ⁣(z)(r+4)!+z(2r2+11r+15)Kν(r+3) ⁣(z)(r+3)!+(r(r+4)z2ν2+4)Kν(r+2) ⁣(z)(r+2)!2zKν(r+1) ⁣(z)(r+1)!Kν(r) ⁣(z)r!=0{z}^{2} \left({r}^{2} + 7 r + 12\right) \frac{K^{(r + 4)}_{\nu}\!\left(z\right)}{\left(r + 4\right)!} + z \left(2 {r}^{2} + 11 r + 15\right) \frac{K^{(r + 3)}_{\nu}\!\left(z\right)}{\left(r + 3\right)!} + \left(r \left(r + 4\right) - {z}^{2} - {\nu}^{2} + 4\right) \frac{K^{(r + 2)}_{\nu}\!\left(z\right)}{\left(r + 2\right)!} - 2 z \frac{K^{(r + 1)}_{\nu}\!\left(z\right)}{\left(r + 1\right)!} - \frac{K^{(r)}_{\nu}\!\left(z\right)}{r !} = 0
Assumptions: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}
TeX:
{z}^{2} \left({r}^{2} + 7 r + 12\right) \frac{K^{(r + 4)}_{\nu}\!\left(z\right)}{\left(r + 4\right)!} + z \left(2 {r}^{2} + 11 r + 15\right) \frac{K^{(r + 3)}_{\nu}\!\left(z\right)}{\left(r + 3\right)!} + \left(r \left(r + 4\right) - {z}^{2} - {\nu}^{2} + 4\right) \frac{K^{(r + 2)}_{\nu}\!\left(z\right)}{\left(r + 2\right)!} - 2 z \frac{K^{(r + 1)}_{\nu}\!\left(z\right)}{\left(r + 1\right)!} - \frac{K^{(r)}_{\nu}\!\left(z\right)}{r !} = 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
Powab{a}^{b} Power
BesselKKν ⁣(z)K_{\nu}\!\left(z\right) Modified Bessel function of the second kind
Factorialn!n ! Factorial
CCC\mathbb{C} Complex numbers
ZZGreaterEqualZn\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
Entry(ID("7377c8"),
    Formula(Equal(Sub(Sub(Add(Add(Mul(Mul(Pow(z, 2), Add(Add(Pow(r, 2), Mul(7, r)), 12)), Div(BesselK(nu, z, Add(r, 4)), Factorial(Add(r, 4)))), Mul(Mul(z, Add(Add(Mul(2, Pow(r, 2)), Mul(11, r)), 15)), Div(BesselK(nu, z, Add(r, 3)), Factorial(Add(r, 3))))), Mul(Add(Sub(Sub(Mul(r, Add(r, 4)), Pow(z, 2)), Pow(nu, 2)), 4), Div(BesselK(nu, z, Add(r, 2)), Factorial(Add(r, 2))))), Mul(Mul(2, z), Div(BesselK(nu, z, Add(r, 1)), Factorial(Add(r, 1))))), Div(BesselK(nu, z, r), Factorial(r))), 0)),
    Variables(nu, z, r),
    Assumptions(And(Element(nu, CC), Element(z, SetMinus(CC, Set(0))), 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.

2019-11-11 15:50:15.016492 UTC