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# AiryAiPrime

 AiryAiPrime[z]gives the derivative of the Airy function .
• 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.
Evaluate numerically:
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:
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:
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:
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:
Nested integrals of the square of AiryAiPrime:
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