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Fungrim entry: 20e530

Ai ⁣(z)=Ai ⁣(0)0F1 ⁣(13,z39)+z22Ai ⁣(0)0F1 ⁣(53,z39)\operatorname{Ai}'\!\left(z\right) = \operatorname{Ai}'\!\left(0\right) \,{}_0F_1\!\left(\frac{1}{3}, \frac{{z}^{3}}{9}\right) + \frac{{z}^{2}}{2} \operatorname{Ai}\!\left(0\right) \,{}_0F_1\!\left(\frac{5}{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{1}{3}, \frac{{z}^{3}}{9}\right) + \frac{{z}^{2}}{2} \operatorname{Ai}\!\left(0\right) \,{}_0F_1\!\left(\frac{5}{3}, \frac{{z}^{3}}{9}\right)

z \in \mathbb{C}
Definitions:
Fungrim symbol Notation Short description
Hypergeometric0F10F1 ⁣(a,z)\,{}_0F_1\!\left(a, z\right) Confluent hypergeometric limit function
Powab{a}^{b} Power
AiryAiAi ⁣(z)\operatorname{Ai}\!\left(z\right) Airy function of the first kind
CCC\mathbb{C} Complex numbers
Source code for this entry:
Entry(ID("20e530"),
    Formula(Equal(AiryAiPrime(z), Add(Mul(AiryAiPrime(0), Hypergeometric0F1(Div(1, 3), Div(Pow(z, 3), 9))), Mul(Mul(Div(Pow(z, 2), 2), AiryAi(0)), Hypergeometric0F1(Div(5, 3), Div(Pow(z, 3), 9)))))),
    Variables(z),
    Assumptions(Element(z, CC)))

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2019-08-21 11:44:15.926409 UTC