BUILT-IN MATHEMATICA SYMBOL

AiryBiPrime

AiryBiPrime[z]
gives the derivative of the Airy function

.

MORE INFORMATION

Mathematical function, suitable for both symbolic and numerical manipulation.

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

AiryBiPrime can be evaluated to arbitrary numerical precision.

AiryBiPrime 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:

AiryBiPrime 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)

AiryBiPrime can be applied to power series:

Applications (2)

Solve differential equations in terms of AiryBiPrime:

Solution of the modified linearized for any function

:

Verify the solution:

Properties & Relations (7)

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 AiryBiPrime:

Generate Airy functions from differential equations:

Integrals:

Integral transforms:

Obtain AiryBiPrime from sums:

AiryBiPrime 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 AiryBiPrime: