Fungrim entry: bd319e

\operatorname{Bi}\!\left(z\right) = \operatorname{Bi}\!\left(0\right) \,{}_0F_1\!\left(\frac{2}{3}, \frac{{z}^{3}}{9}\right) + z \operatorname{Bi}'\!\left(0\right) \,{}_0F_1\!\left(\frac{4}{3}, \frac{{z}^{3}}{9}\right)

Assumptions:

z \in \mathbb{C}

TeX:

\operatorname{Bi}\!\left(z\right) = \operatorname{Bi}\!\left(0\right) \,{}_0F_1\!\left(\frac{2}{3}, \frac{{z}^{3}}{9}\right) + z \operatorname{Bi}'\!\left(0\right) \,{}_0F_1\!\left(\frac{4}{3}, \frac{{z}^{3}}{9}\right)

z \in \mathbb{C}

Definitions:

Fungrim symbol	Notation	Short description
`AiryBi`	$\operatorname{Bi}\!\left(z\right)$	Airy function of the second 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("bd319e"),
    Formula(Equal(AiryBi(z), Add(Mul(AiryBi(0), Hypergeometric0F1(Div(2, 3), Div(Pow(z, 3), 9))), Mul(Mul(z, AiryBi(0, 1)), Hypergeometric0F1(Div(4, 3), Div(Pow(z, 3), 9)))))),
    Variables(z),
    Assumptions(Element(z, CC)))

Topics using this entry

Airy functions