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Fungrim entry: a047eb

1F1 ⁣(a,b,z)=ez1F1 ⁣(ba,b,z)\,{}_1{\textbf F}_1\!\left(a, b, z\right) = {e}^{z} \,{}_1{\textbf F}_1\!\left(b - a, b, -z\right)
Assumptions:aC  and  bC  and  zCa \in \mathbb{C} \;\mathbin{\operatorname{and}}\; b \in \mathbb{C} \;\mathbin{\operatorname{and}}\; z \in \mathbb{C}
\,{}_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}
Fungrim symbol Notation Short description
Hypergeometric1F1Regularized1F1 ⁣(a,b,z)\,{}_1{\textbf F}_1\!\left(a, b, z\right) Regularized Kummer confluent hypergeometric function
Expez{e}^{z} Exponential function
CCC\mathbb{C} Complex numbers
Source code for this entry:
    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))))

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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