Evaluate numerically to high precision:

The precision of the output tracks the precision of the input:

Evaluate for complex arguments:

Evaluate AiryAi efficiently at high precision:

Compute worst-case guaranteed intervals using Interval and CenteredInterval objects:

Or compute average-case statistical intervals using Around:

Compute the elementwise values of an array:

Or compute the matrix AiryAi function using MatrixFunction:

Simple exact values are generated automatically:

Limiting values at infinity:

The first three zeros:

Find a zero of AiryAi using Solve:

Plot the AiryAi function:

Plot the real part of :

Plot the imaginary part of :

AiryAi is defined for all real and complex values:

Approximate function range of AiryAi:

AiryAi is an analytic function of x:

AiryAi is neither non-increasing nor non-decreasing:

AiryAi is not injective:

AiryAi is not surjective:

AiryAi is neither non-negative nor non-positive:

AiryAi has no singularities or discontinuities:

AiryAi is neither convex nor concave:

First derivative:

Higher derivatives:

Formula for the derivative:

Indefinite integral of AiryAi:

Verify the anti-derivative:

Definite integral of AiryAi:

More integrals:

Taylor expansion for AiryAi:

Plot the first three approximations for AiryAi around :

General term in the series expansion of AiryAi:

Find the series expansion at infinity:

Find the series expansion at infinity for an arbitrary symbolic direction :

AiryAi can be applied to power series:

Compute the Fourier transform using FourierTransform:

MellinTransform:

HankelTransform:

Simplify the expression to AiryAi:

FunctionExpand tries to simplify the argument of AiryAi:

Functional identity:

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: