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Fungrim entry: c8fcc7

U ⁣(a,b,z)=zaU ⁣(a,b,z)U^{*}\!\left(a, b, z\right) = {z}^{a} U\!\left(a, b, 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
U^{*}\!\left(a, b, z\right) = {z}^{a} U\!\left(a, b, 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
Fungrim symbol Notation Short description
HypergeometricUStarU ⁣(a,b,z)U^{*}\!\left(a, b, z\right) Scaled Tricomi confluent hypergeometric function
Powab{a}^{b} Power
HypergeometricUU ⁣(a,b,z)U\!\left(a, b, z\right) Tricomi confluent hypergeometric function
CCC\mathbb{C} Complex numbers
Source code for this entry:
    Formula(Equal(HypergeometricUStar(a, b, z), Mul(Pow(z, a), HypergeometricU(a, b, 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.

2021-03-15 19:12:00.328586 UTC