This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# AiryBi

 AiryBi[z]gives the Airy function .
• Mathematical function, suitable for both symbolic and numerical manipulation.
• The Airy function is a solution to the differential equation .
• increases exponentially as .
• AiryBi[z] is an entire function of z with no branch cut discontinuities.
• For certain special arguments, AiryBi automatically evaluates to exact values.
• AiryBi can be evaluated to arbitrary numerical precision.
• AiryBi automatically threads over lists.
Evaluate numerically:
Evaluate numerically:
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 Scope   (7)
Evaluate for complex arguments:
Evaluate to high precision:
The precision of the output tracks the precision of the input:
AiryBi threads element-wise over lists and matrices:
Simple exact values are generated automatically:
Find series expansions at infinity:
AiryBi can be applied to power series:
Expansion at infinity for an arbitrary symbolic direction :
 Applications   (3)
Solve the Schrödinger equation in a linear potential (e.g. uniform electric field):
Check the Sommerfeld radiation condition for a combination of Airy functions:
There is only an outgoing plane wave:
Plot the imaginary part in the complex plane:
Use FullSimplify to simplify Airy functions, here in the Wronskian of the Airy equation:
Compare with the output of Wronskian:
FunctionExpand tries to simplify the argument of AiryBi:
Generate Airy functions from differential equations:
Find a numerical root:
Compare with the built-in function AiryBiZero:
Integrals:
Integral transforms:
Machine-precision input is insufficient to get a correct answer: