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

Airy functions