# Fungrim entry: 01bbb6

$\operatorname{Ai}\!\left(z\right) = \operatorname{Ai}\!\left(0\right) \,{}_0F_1\!\left(\frac{2}{3}, \frac{{z}^{3}}{9}\right) + z \operatorname{Ai}'\!\left(0\right) \,{}_0F_1\!\left(\frac{4}{3}, \frac{{z}^{3}}{9}\right)$
Assumptions:$z \in \mathbb{C}$
TeX:
\operatorname{Ai}\!\left(z\right) = \operatorname{Ai}\!\left(0\right) \,{}_0F_1\!\left(\frac{2}{3}, \frac{{z}^{3}}{9}\right) + z \operatorname{Ai}'\!\left(0\right) \,{}_0F_1\!\left(\frac{4}{3}, \frac{{z}^{3}}{9}\right)

z \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
AiryAi$\operatorname{Ai}\!\left(z\right)$ Airy function of the first kind
Hypergeometric0F1$\,{}_0F_1\!\left(a, z\right)$ Confluent hypergeometric limit function
Pow${a}^{b}$ Power
CC$\mathbb{C}$ Complex numbers
Source code for this entry:
Entry(ID("01bbb6"),
Formula(Equal(AiryAi(z), Add(Mul(AiryAi(0), Hypergeometric0F1(Div(2, 3), Div(Pow(z, 3), 9))), Mul(Mul(z, AiryAi(0, 1)), Hypergeometric0F1(Div(4, 3), Div(Pow(z, 3), 9)))))),
Variables(z),
Assumptions(Element(z, CC)))

## Topics using this entry

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