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Fungrim entry: 325a0e

0F1 ⁣(a,z)=(z)(1a)/2Ja1 ⁣(2z)\,{}_0{\textbf F}_1\!\left(a, z\right) = {\left(-z\right)}^{\left( 1 - a \right) / 2} J_{a - 1}\!\left(2 \sqrt{-z}\right)
Assumptions:aCandzCandz0a \in \mathbb{C} \,\mathbin{\operatorname{and}}\, z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, z \ne 0
TeX:
\,{}_0{\textbf F}_1\!\left(a, z\right) = {\left(-z\right)}^{\left( 1 - a \right) / 2} J_{a - 1}\!\left(2 \sqrt{-z}\right)

a \in \mathbb{C} \,\mathbin{\operatorname{and}}\, z \in \mathbb{C} \,\mathbin{\operatorname{and}}\, z \ne 0
Definitions:
Fungrim symbol Notation Short description
Hypergeometric0F1Regularized0F1 ⁣(a,z)\,{}_0{\textbf F}_1\!\left(a, z\right) Regularized confluent hypergeometric limit function
Powab{a}^{b} Power
BesselJJν ⁣(z)J_{\nu}\!\left(z\right) Bessel function of the first kind
Sqrtz\sqrt{z} Principal square root
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("325a0e"),
    Formula(Equal(Hypergeometric0F1Regularized(a, z), Mul(Pow(Neg(z), Div(Sub(1, a), 2)), BesselJ(Sub(a, 1), Mul(2, Sqrt(Neg(z))))))),
    Variables(a, z),
    Assumptions(And(Element(a, CC), Element(z, CC), Unequal(z, 0))))

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

2019-08-21 11:44:15.926409 UTC