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Fungrim entry: 4cf1e9

U ⁣(a,b,z)=2F0 ⁣(a,ab+1,1z)U^{*}\!\left(a, b, z\right) = \,{}_2F_0\!\left(a, a - b + 1, -\frac{1}{z}\right)
Assumptions:aC  and  bC  and  zC  and  z0a \in \mathbb{C} \;\mathbin{\operatorname{and}}\; b \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \ne 0
TeX:
U^{*}\!\left(a, b, z\right) = \,{}_2F_0\!\left(a, a - b + 1, -\frac{1}{z}\right)

a \in \mathbb{C} \;\mathbin{\operatorname{and}}\; b \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \ne 0
Definitions:
Fungrim symbol Notation Short description
HypergeometricUStarU ⁣(a,b,z)U^{*}\!\left(a, b, z\right) Scaled Tricomi confluent hypergeometric function
Hypergeometric2F02F0 ⁣(a,b,z)\,{}_2F_0\!\left(a, b, z\right) Tricomi confluent hypergeometric function, alternative notation
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("4cf1e9"),
    Formula(Equal(HypergeometricUStar(a, b, z), Hypergeometric2F0(a, Add(Sub(a, b), 1), Neg(Div(1, z))))),
    Variables(a, b, z),
    Assumptions(And(Element(a, CC), Element(b, CC), Element(z, CC), NotEqual(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.

2020-04-08 16:14:44.404316 UTC