AiryAi
AiryAi[z]
gives the Airy function .
Details

- Mathematical function, suitable for both symbolic and numerical manipulation.
- The Airy function
is a solution to the differential equation
.
tends to zero as
.
- AiryAi[z] is an entire function of z with no branch cut discontinuities.
- For certain special arguments, AiryAi automatically evaluates to exact values.
- AiryAi can be evaluated to arbitrary numerical precision.
- AiryAi automatically threads over lists.
Examples
open allclose allBasic Examples (5)
Plot over a subset of the reals:
Plot over a subset of the complexes:
Series expansion at the origin:
Series expansion at Infinity:
Scope (34)
Numerical Evaluation (4)
Specific Values (4)
Visualization (2)
Function Properties (2)
Integration (3)
Series Expansions (5)
Integral Transforms (3)
Function Identities and Simplifications (3)
Simplify the expression to AiryAi:
FunctionExpand tries to simplify the argument of AiryAi:
Function Representations (5)
Integral representation for real argument:
Relationship to Bessel functions:
AiryAi can be represented as a DifferentialRoot:
AiryAi can be represented in terms of MeijerG:
TraditionalForm formatting:
Applications (3)
Solve the Schrödinger equation in a linear potential (e.g. uniform electric field):
Plot the absolute value in the complex plane:
Nested integrals of the square of AiryAi:
Properties & Relations (8)
Use FullSimplify to simplify expressions involving Airy functions:
Compare with the output of Wronskian:
FunctionExpand tries to simplify the argument of AiryAi:
Solve the Airy differential equation:
Compare with built-in function AiryAiZero:
AiryAi can be represented as a DifferentialRoot:
Possible Issues (5)
Machine-precision input is insufficient to get a correct answer:
Use arbitrary-precision evaluation instead:
A larger setting for $MaxExtraPrecision can be needed:

Machine-number inputs can give high‐precision results:
Simplifications sometimes hold only in parts of the complex plane:
Parentheses are required when inputting in the traditional form:
Text
Wolfram Research (1988), AiryAi, Wolfram Language function, https://reference.wolfram.com/language/ref/AiryAi.html.
BibTeX
BibLaTeX
CMS
Wolfram Language. 1988. "AiryAi." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/AiryAi.html.
APA
Wolfram Language. (1988). AiryAi. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/AiryAi.html