Fungrim entry: a047eb

\,{}_1{\textbf F}_1\!\left(a, b, z\right) = {e}^{z} \,{}_1{\textbf F}_1\!\left(b - a, b, -z\right)

Assumptions:

a \in \mathbb{C} \;\mathbin{\operatorname{and}}\; b \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C}

TeX:

\,{}_1{\textbf F}_1\!\left(a, b, z\right) = {e}^{z} \,{}_1{\textbf F}_1\!\left(b - a, b, -z\right)

a \in \mathbb{C} \;\mathbin{\operatorname{and}}\; b \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C}

Definitions:

Fungrim symbol	Notation	Short description
`Hypergeometric1F1Regularized`	$\,{}_1{\textbf F}_1\!\left(a, b, z\right)$	Regularized Kummer confluent hypergeometric function
`Exp`	${e}^{z}$	Exponential function
`CC`	$\mathbb{C}$	Complex numbers

Source code for this entry:

Entry(ID("a047eb"),
    Formula(Equal(Hypergeometric1F1Regularized(a, b, z), Mul(Exp(z), Hypergeometric1F1Regularized(Sub(b, a), b, Neg(z))))),
    Variables(a, b, z),
    Assumptions(And(Element(a, CC), Element(b, CC), Element(z, CC))))

Topics using this entry

Confluent hypergeometric functions