Fungrim entry: 58d91f

I'_{\nu}\!\left(z\right) = \frac{I_{\nu - 1}\!\left(z\right) + I_{\nu + 1}\!\left(z\right)}{2}

Assumptions:

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

Alternative assumptions:

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

TeX:

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\}

Definitions:

Fungrim symbol	Notation	Short description
`BesselIDerivative`	$I^{(r)}_{\nu}\!\left(z\right)$	Differentiated modified Bessel function of the first kind
`BesselI`	$I_{\nu}\!\left(z\right)$	Modified Bessel function of the first kind
`ZZ`	$\mathbb{Z}$	Integers
`CC`	$\mathbb{C}$	Complex numbers

Source code for this entry:

Entry(ID("58d91f"),
    Formula(Equal(BesselIDerivative(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))))))

Fungrim entry: 58d91f

Topics using this entry