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Fungrim entry: be533c

1F1 ⁣(a,b,z)=ez1F1 ⁣(ba,b,z)\,{}_1F_1\!\left(a, b, z\right) = {e}^{z} \,{}_1F_1\!\left(b - a, b, -z\right)
Assumptions:aCandbC{0,1,}andzCa \in \mathbb{C} \,\mathbin{\operatorname{and}}\, b \in \mathbb{C} \setminus \{0, -1, \ldots\} \,\mathbin{\operatorname{and}}\, z \in \mathbb{C}
TeX:
\,{}_1F_1\!\left(a, b, z\right) = {e}^{z} \,{}_1F_1\!\left(b - a, b, -z\right)

a \in \mathbb{C} \,\mathbin{\operatorname{and}}\, b \in \mathbb{C} \setminus \{0, -1, \ldots\} \,\mathbin{\operatorname{and}}\, z \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
Hypergeometric1F11F1 ⁣(a,b,z)\,{}_1F_1\!\left(a, b, z\right) Kummer confluent hypergeometric function
Expez{e}^{z} Exponential function
CCC\mathbb{C} Complex numbers
ZZLessEqualZn\mathbb{Z}_{\le n} Integers less than or equal to n
Source code for this entry:
Entry(ID("be533c"),
    Formula(Equal(Hypergeometric1F1(a, b, z), Mul(Exp(z), Hypergeometric1F1(Sub(b, a), b, Neg(z))))),
    Variables(a, b, z),
    Assumptions(And(Element(a, CC), Element(b, SetMinus(CC, ZZLessEqual(0))), 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.

2019-10-05 13:11:19.856591 UTC