BUILT-IN MATHEMATICA SYMBOL

AiryAiPrime

AiryAiPrime[z]
gives the derivative of the Airy function

.

MORE INFORMATION

Mathematical function, suitable for both symbolic and numerical manipulation.

For certain special arguments, AiryAiPrime automatically evaluates to exact values.

AiryAiPrime can be evaluated to arbitrary numerical precision.

AiryAiPrime automatically threads over lists.

EXAMPLES

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Basic Examples (3)

Evaluate numerically:

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Scope (6)

Evaluate for complex arguments:

Evaluate to high precision:

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

AiryAiPrime threads element-wise over lists:

Simple exact values are generated automatically:

Find series expansions at infinity:

The behavior at negative infinity is quite different:

TraditionalForm formatting:

Generalizations & Extensions (1)

AiryAiPrime can be applied to power series:

Applications (5)

A plot of the absolute value of AiryAiPrime over the complex plane:

Solve differential equations in terms of AiryAiPrime:

Solution of the time-independent Schrödinger equation in a linear cone potential:

The normalizable states are determined through the zeros of AiryAiPrime:

Plot the normalizable states:

An integral kernel related to the Gaussian unitary ensembles:

A convolution integral solving the modified linearized for any function

:

Verify solution:

Properties & Relations (6)

Use FullSimplify to simplify Airy functions, here in the of the Airy equation:

Compare with the output of Wronskian:

FunctionExpand tries to simplify the argument of AiryAiPrime:

Airy functions are generated as solutions by DSolve:

Integrals:

Integral transforms:

Obtain AiryAiPrime from sums:

AiryAiPrime appears in special cases of several mathematical functions:

Possible Issues (3)

Machine-precision input is insufficient to give a correct answer:

Use arbitrary-precision evaluation instead:

A larger setting for $MaxExtraPrecision can be needed:

Machine-number inputs can give high-precision results:

Neat Examples (1)

Nested integrals of the square of AiryAiPrime: