Fungrim home page

Fungrim entry: 4fb391

Iν ⁣(z)=z2ν(Iν1 ⁣(z)Iν+1 ⁣(z))I_{\nu}\!\left(z\right) = \frac{z}{2 \nu} \left(I_{\nu - 1}\!\left(z\right) - I_{\nu + 1}\!\left(z\right)\right)
Assumptions:νZ{0}andzC\nu \in \mathbb{Z} \setminus \left\{0\right\} \,\mathbin{\operatorname{and}}\, z \in \mathbb{C}
Alternative assumptions:νC{0}andzC{0}\nu \in \mathbb{C} \setminus \left\{0\right\} \,\mathbin{\operatorname{and}}\, z \in \mathbb{C} \setminus \left\{0\right\}
TeX:
I_{\nu}\!\left(z\right) = \frac{z}{2 \nu} \left(I_{\nu - 1}\!\left(z\right) - I_{\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\}
Definitions:
Fungrim symbol Notation Short description
BesselIIν ⁣(z)I_{\nu}\!\left(z\right) Modified Bessel function of the first kind
ZZZ\mathbb{Z} Integers
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("4fb391"),
    Formula(Equal(BesselI(nu, z), Mul(Div(z, Mul(2, nu)), Sub(BesselI(Sub(nu, 1), z), BesselI(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))))))

Topics using this entry

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

2019-09-15 11:00:55.020619 UTC