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

Confluent hypergeometric functions