Fungrim entry: 4cf1e9

U^{*}\!\left(a, b, z\right) = \,{}_2F_0\!\left(a, a - b + 1, -\frac{1}{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) = \,{}_2F_0\!\left(a, a - b + 1, -\frac{1}{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
`Hypergeometric2F0`	$\,{}_2F_0\!\left(a, b, z\right)$	Tricomi confluent hypergeometric function, alternative notation
`CC`	$\mathbb{C}$	Complex numbers

Source code for this entry:

Entry(ID("4cf1e9"),
    Formula(Equal(HypergeometricUStar(a, b, z), Hypergeometric2F0(a, Add(Sub(a, b), 1), Neg(Div(1, 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