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

Airy functions