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Fungrim entry: 58d91f

Iν ⁣(z)=Iν1 ⁣(z)+Iν+1 ⁣(z)2I'_{\nu}\!\left(z\right) = \frac{I_{\nu - 1}\!\left(z\right) + I_{\nu + 1}\!\left(z\right)}{2}
Assumptions:νZ  and  zC\nu \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C}
Alternative assumptions:νC  and  zC{0}\nu \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C} \setminus \left\{0\right\}
I'_{\nu}\!\left(z\right) = \frac{I_{\nu - 1}\!\left(z\right) + I_{\nu + 1}\!\left(z\right)}{2}

\nu \in \mathbb{Z} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C}

\nu \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C} \setminus \left\{0\right\}
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:
    Formula(Equal(BesselI(nu, z, 1), Div(Add(BesselI(Sub(nu, 1), z), BesselI(Add(nu, 1), z)), 2))),
    Variables(nu, z),
    Assumptions(And(Element(nu, ZZ), Element(z, CC)), And(Element(nu, CC), Element(z, SetMinus(CC, Set(0))))))

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

2021-03-15 19:12:00.328586 UTC