This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
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gives the Airy function .
  • 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.
Evaluate numerically:
Evaluate numerically:
Click for copyable input
Click for copyable input
Click for copyable input
Evaluate for complex arguments:
Evaluate to high precision:
The precision of the output tracks the precision of the input:
AiryAi threads element-wise over lists:
Simple exact values are generated automatically:
Find series expansions at infinity:
TraditionalForm formatting:
AiryAi can be applied to power series:
Find series expansions at infinity for an arbitrary symbolic direction :
Solve the Schrödinger equation in a linear potential (e.g. uniform electric field):
Plot the absolute value in the complex plane:
Plot the imaginary part in the complex plane:
Nested integrals of the square of AiryAi:
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:
Find a numerical root:
Compare with built-in function AiryAiZero:
Verify the anti-derivative:
Integral transforms:
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:
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