AiryAi

Generated from the engine's own definition: compute-engine's symbol, which we neither extend nor document by hand.

Airy function of the first kind

✓ checked against that system · ! checked, with disagreements (hover a chip)WikipediaAiry function↗Airy function of the first kind↗MathWorldAiryFunctions↗AiryAi↗WikidataQ109729241↗DLMF9.2.i↗FungrimAiryAi↗Fungrim entryWolfram LanguageAiryAi✓↗

AiryAi(complex | infinity) -> numberAs native, and keeps its digits past a double's for real argument (N(AiryAi(2), 50)).

SageMathairy_ai(complex | infinity)mpmathairyai(complex | infinity)Juliaenumeratio_ball(airy_ai, complex | infinity)

Typed signatures

Type	Package	Applies
(complex | infinity) -> number	analyticreplaces compute-engine	always
(complex | infinity) -> number	compute-engine	always

Domain: Compute engine

Plot

the complex plot cannot lower AiryAi

Examples

Basic #

$\mathrm{Ai}(0) = 3^{-2/3}/\Gamma(2/3)$ numerically

live ↗

In$N(\operatorname{Ai}(0))$Out$0.355\,028\,053\,887\,817\,2$

Known value · mpmath 1.3.0 airyai

live ↗

In$N(\operatorname{Ai}(1))$Out$0.135\,292\,416\,312\,881\,41$

Known value · mpmath 1.3.0 airyai

live ↗

In$\operatorname{Series}(\operatorname{Ai}(x), x, 0, 4)$Out$\frac{1}{Γ(\frac{2}{3})×3^{\frac{2}{3}}}-\frac{x}{Γ(\frac{1}{3})\sqrt[3]{3}}+\frac{x^3}{6Γ(\frac{2}{3})×3^{\frac{2}{3}}}-\frac{x^4}{12Γ(\frac{1}{3})\sqrt[3]{3}}+O\left(x^6\right)$

live ↗

In$\operatorname{Normal}(\operatorname{Series}(\operatorname{Ai}(x), x, ∞, 2))$Out$(\frac{1}{2\sqrt{π}\sqrt[4]{x}}-\frac{5}{96\sqrt{π}x^{\frac{7}{4}}})e^{-\frac{1}{3}×2x^{3/2}}$

Scope #

live ↗

In$N(\operatorname{Ai}(2), 50)$Out$0.034\,924\,130\,423\,274\,379\,135\,322\,080\,791\,807\,609\,761\,060\,213\,897\,583$

live ↗

In$N(\mathrm{FunctionRange}(\operatorname{Ai}(x), x, y))$Out$-0.419\,015\,478\,032\,563\,95≤y≤0.535\,656\,656\,015\,699\,9$

live ↗

In$\frac{\mathrm{d}\operatorname{Ai}(x)}{\mathrm{d}x}$Out$\operatorname{Ai}'(x)$

live ↗

In$\operatorname{Series}(\operatorname{Ai}(x), x, 0, 7)$Out$\frac{1}{Γ(\frac{2}{3})×3^{\frac{2}{3}}}-\frac{x}{Γ(\frac{1}{3})\sqrt[3]{3}}+\frac{x^3}{6Γ(\frac{2}{3})×3^{\frac{2}{3}}}-\frac{x^4}{12Γ(\frac{1}{3})\sqrt[3]{3}}+\frac{x^6}{180Γ(\frac{2}{3})×3^{\frac{2}{3}}}-\frac{x^7}{504Γ(\frac{1}{3})\sqrt[3]{3}}+O\left(x^9\right)$

About

Examples	8
Checked against	Wolfram Language 8 agreeSageMath 6 agree1 unevaluatedmpmath 3 agreeJulia 3 agree
Crosswalk	Wikipedia ×2MathWorld ×2WikidataDLMFFungrimFungrim entry ×12Wolfram LanguageSageMathmpmathJulia

Implementation

mappedmpmathpackages/oracle/src/mappings.ts

mappedsagepackages/oracle/src/mappings.ts

mappedjuliapackages/oracle/src/mappings.ts