# Fungrim entry: 9d3147

$U\!\left(a, b, z\right) = {z}^{1 - b} U\!\left(1 + a - b, 2 - b, z\right)$
Assumptions:$a \in \mathbb{C} \;\mathbin{\operatorname{and}}\; b \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \ne 0$
TeX:
U\!\left(a, b, z\right) = {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
Definitions:
Fungrim symbol Notation Short description
HypergeometricU$U\!\left(a, b, z\right)$ Tricomi confluent hypergeometric function
Pow${a}^{b}$ Power
CC$\mathbb{C}$ Complex numbers
Source code for this entry:
Entry(ID("9d3147"),
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), NotEqual(z, 0))))

## Topics using this entry

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