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Fungrim entry: 5d9c43

I1/2 ⁣(z)=(2zπ)1/2cosh ⁣(z)zI_{-1 / 2}\!\left(z\right) = {\left(\frac{2 z}{\pi}\right)}^{1 / 2} \frac{\cosh\!\left(z\right)}{z}
Assumptions:zC{0}z \in \mathbb{C} \setminus \left\{0\right\}
TeX:
I_{-1 / 2}\!\left(z\right) = {\left(\frac{2 z}{\pi}\right)}^{1 / 2} \frac{\cosh\!\left(z\right)}{z}

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
Powab{a}^{b} Power
ConstPiπ\pi The constant pi (3.14...)
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("5d9c43"),
    Formula(Equal(BesselI(Neg(Div(1, 2)), z), Mul(Pow(Div(Mul(2, z), ConstPi), Div(1, 2)), Div(Cosh(z), z)))),
    Variables(z),
    Assumptions(Element(z, SetMinus(CC, Set(0)))))

Topics using this entry

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2019-09-20 18:07:53.062439 UTC