Fungrim entry: c8fcc7

U^{*}\!\left(a, b, z\right) = {z}^{a} U\!\left(a, 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}^{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

Definitions:

Fungrim symbol	Notation	Short description
`HypergeometricUStar`	$U^{*}\!\left(a, b, z\right)$	Scaled Tricomi confluent hypergeometric function
`Pow`	${a}^{b}$	Power
`HypergeometricU`	$U\!\left(a, b, z\right)$	Tricomi confluent hypergeometric function
`CC`	$\mathbb{C}$	Complex numbers

Source code for this entry:

Entry(ID("c8fcc7"),
    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))))

Topics using this entry

Confluent hypergeometric functions