Airy Function Zeros

Author

Eric W. Weisstein
January 24, 2007

This notebook downloaded from http://mathworld.wolfram.com/notebooks/SpecialFunctions/AiryFunctionZeros.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/AiryFunctionZeros.html.

©2007 Wolfram Research, Inc. except for portions noted otherwise

Plots

Ai and Bi

roots=PlotRoots[#[z],{z,-10,2},DisplayFunction->Identity]&/@{AiryAi,AiryBi}

N[AiryAiZero[Range[6]],10]

N[AiryBiZero[Range[7]],10]

Show[Block[{$DisplayFunction=Identity},
{
Plot[AiryAi[z],{z,-10,2},PlotStyle->Red],
Plot[AiryBi[z],{z,-10,2},PlotStyle->Blue],
Graphics[{
{Red,PointSize[.025],Point[{#,AiryAi[#]}]&/@roots[[1]]},
{Blue,PointSize[.025],Point[{#,AiryBi[#]}]&/@roots[[2]]}
}
]
}],
AxesLabel->TraditionalForm/@{x,{StyleForm[AiryAi[x],FontColor->Red],
StyleForm[AiryBi[x],FontColor->Blue]}}
]

Real Axis

Ai(x) and Bi(x)

Plot[{AiryAi[x],AiryBi[x]},{x,-10,3},PlotStyle->{Red,Blue}]

Zeros

<<Utilities`Plot`

Reverse[PlotRoots[AiryAi[z],{z,-10,2}]]

FindRoot[AiryAi[z],{z,-2.338107410459767`},WorkingPrecision->100]

Bi

<<Utilities`Plot`

Reverse[PlotRoots[AiryBi[z],{z,-10,2}]]

FindRoot[AiryBi[z],{z,-1.173713222709128`},WorkingPrecision->100]