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Fungrim entry: 51b241

y(z)zy(z)=0   where y(z)=CAi ⁣(z)+DBi ⁣(z)y''(z) - z y(z) = 0\; \text{ where } y(z) = C \operatorname{Ai}\!\left(z\right) + D \operatorname{Bi}\!\left(z\right)
Assumptions:zC  and  CC  and  DCz \in \mathbb{C} \;\mathbin{\operatorname{and}}\; C \in \mathbb{C} \;\mathbin{\operatorname{and}}\; D \in \mathbb{C}
y''(z) - z y(z) = 0\; \text{ where } y(z) = C \operatorname{Ai}\!\left(z\right) + D \operatorname{Bi}\!\left(z\right)

z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; C \in \mathbb{C} \;\mathbin{\operatorname{and}}\; D \in \mathbb{C}
Fungrim symbol Notation Short description
ComplexDerivativeddzf ⁣(z)\frac{d}{d z}\, f\!\left(z\right) Complex derivative
AiryAiAi ⁣(z)\operatorname{Ai}\!\left(z\right) Airy function of the first kind
AiryBiBi ⁣(z)\operatorname{Bi}\!\left(z\right) Airy function of the second kind
CCC\mathbb{C} Complex numbers
Source code for this entry:
    Formula(Where(Equal(Sub(ComplexDerivative(y(z), For(z, z, 2)), Mul(z, y(z))), 0), Equal(y(z), Add(Mul(C, AiryAi(z)), Mul(D, AiryBi(z)))))),
    Variables(z, C, D),
    Assumptions(And(Element(z, CC), Element(C, CC), Element(D, CC))))

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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