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Fungrim entry: 9d3147

U ⁣(a,b,z)=z1bU ⁣(1+ab,2b,z)U\!\left(a, b, z\right) = {z}^{1 - b} U\!\left(1 + a - b, 2 - b, z\right)
Assumptions:aCandbCandzCandz0a \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}^{1 - b} U\!\left(1 + a - b, 2 - 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
HypergeometricUU ⁣(a,b,z)U\!\left(a, b, z\right) Tricomi confluent hypergeometric function
Powab{a}^{b} Power
CCC\mathbb{C} Complex numbers
Source code for this entry:
    Formula(Equal(HypergeometricU(a, b, z), Mul(Pow(z, Sub(1, b)), HypergeometricU(Sub(Add(1, a), b), Sub(2, b), z)))),
    Variables(a, b, z),
    Assumptions(And(Element(a, CC), Element(b, 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.

2019-10-05 13:11:19.856591 UTC