# Fungrim entry: 51b241

$y''(z) - z y(z) = 0\; \text{ where } y(z) = C \operatorname{Ai}\!\left(z\right) + D \operatorname{Bi}\!\left(z\right)$
Assumptions:$z \in \mathbb{C} \;\mathbin{\operatorname{and}}\; C \in \mathbb{C} \;\mathbin{\operatorname{and}}\; D \in \mathbb{C}$
TeX:
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}
Definitions:
Fungrim symbol Notation Short description
ComplexDerivative$\frac{d}{d z}\, f\!\left(z\right)$ Complex derivative
AiryAi$\operatorname{Ai}\!\left(z\right)$ Airy function of the first kind
AiryBi$\operatorname{Bi}\!\left(z\right)$ Airy function of the second kind
CC$\mathbb{C}$ Complex numbers
Source code for this entry:
Entry(ID("51b241"),
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))))

## Topics using this entry

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