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Fungrim entry: 01bbb6

Ai ⁣(z)=Ai ⁣(0)0F1 ⁣(23,z39)+zAi ⁣(0)0F1 ⁣(43,z39)\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:zCz \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
AiryAiAi ⁣(z)\operatorname{Ai}\!\left(z\right) Airy function of the first kind
Hypergeometric0F10F1 ⁣(a,z)\,{}_0F_1\!\left(a, z\right) Confluent hypergeometric limit function
Powab{a}^{b} Power
CCC\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, AiryAiPrime(0)), Hypergeometric0F1(Div(4, 3), Div(Pow(z, 3), 9)))))),
    Variables(z),
    Assumptions(Element(z, CC)))

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2019-08-21 11:44:15.926409 UTC