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Fungrim entry: 9d98f8

Kν ⁣(z)=z2ν(Kν1 ⁣(z)Kν+1 ⁣(z))K_{\nu}\!\left(z\right) = -\frac{z}{2 \nu} \left(K_{\nu - 1}\!\left(z\right) - K_{\nu + 1}\!\left(z\right)\right)
Assumptions:νZ{0}  and  zC\nu \in \mathbb{Z} \setminus \left\{0\right\} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C}
Alternative assumptions:νC{0}  and  zC{0}\nu \in \mathbb{C} \setminus \left\{0\right\} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C} \setminus \left\{0\right\}
K_{\nu}\!\left(z\right) = -\frac{z}{2 \nu} \left(K_{\nu - 1}\!\left(z\right) - K_{\nu + 1}\!\left(z\right)\right)

\nu \in \mathbb{Z} \setminus \left\{0\right\} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C}

\nu \in \mathbb{C} \setminus \left\{0\right\} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C} \setminus \left\{0\right\}
Fungrim symbol Notation Short description
BesselKKν ⁣(z)K_{\nu}\!\left(z\right) Modified Bessel function of the second kind
ZZZ\mathbb{Z} Integers
CCC\mathbb{C} Complex numbers
Source code for this entry:
    Formula(Equal(BesselK(nu, z), Neg(Mul(Div(z, Mul(2, nu)), Sub(BesselK(Sub(nu, 1), z), BesselK(Add(nu, 1), z)))))),
    Variables(nu, z),
    Assumptions(And(Element(nu, SetMinus(ZZ, Set(0))), Element(z, CC)), And(Element(nu, SetMinus(CC, Set(0))), Element(z, SetMinus(CC, Set(0))))))

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2021-03-15 19:12:00.328586 UTC