WOLFRAM

Wolfram Language & System Documentation Center

AiryBiZero[k]

represents the k^(th) zero of the Airy function TemplateBox[{x}, AiryBi].

AiryBiZero[k,x0]

represents the k^(th) zero less than x0.

Details
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Numerical Evaluation  
Specific Values  
Visualization  
Series Expansion  
Applications  
See Also
Tech Notes
Related Guides
History
Cite this Page

AiryBiZero

AiryBiZero[k]

represents the k^(th) zero of the Airy function TemplateBox[{x}, AiryBi].

AiryBiZero[k,x0]

represents the k^(th) zero less than x0.

Details

  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • N[AiryBiZero[k]] gives a numerical approximation so long as the specified zero exists.
  • AiryBiZero[k] represents the k^(th) zero less than 0.
  • AiryBiZero can be evaluated to arbitrary numerical precision.
  • AiryBiZero automatically threads over lists. »

Examples

open all close all

Basic Examples  (4)

Evaluate numerically:

AiryBiZero gives the zeros of AiryBi:

Display zeros of the AiryBi function over a subset of the reals:

Series expansion at Infinity:

Scope  (11)

Numerical Evaluation  (4)

Find the third zero of TemplateBox[{x}, AiryBi]:

Find the second zero of TemplateBox[{x}, AiryBi] less than :

Evaluate numerically to high precision:

Evaluate efficiently at high precision:

Compute the elementwise values of an array using automatic threading:

Or compute the matrix AiryBiZero function using MatrixFunction:

Compute average-case statistical intervals using Around:

Specific Values  (4)

Limiting value at infinity:

The first three zeros:

Find the first zero of AiryBi using Solve:

AiryBiZero threads elementwise over lists:

Visualization  (2)

Display zeros of AiryBi function:

Show the first zero less than :

Series Expansion  (1)

Asymptotic behavior of AiryBiZero[k] for large k:

Applications  (1)

Display zeros on the plot:

Wolfram Research (2007), AiryBiZero, Wolfram Language function, https://reference.wolfram.com/language/ref/AiryBiZero.html.

Text

Wolfram Research (2007), AiryBiZero, Wolfram Language function, https://reference.wolfram.com/language/ref/AiryBiZero.html.

CMS

Wolfram Language. 2007. "AiryBiZero." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/AiryBiZero.html.

APA

Wolfram Language. (2007). AiryBiZero. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/AiryBiZero.html

BibTeX

@misc{reference.wolfram_2025_airybizero, author="Wolfram Research", title="{AiryBiZero}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/AiryBiZero.html}", note=[Accessed: 07-August-2025]}

BibLaTeX

@online{reference.wolfram_2025_airybizero, organization={Wolfram Research}, title={AiryBiZero}, year={2007}, url={https://reference.wolfram.com/language/ref/AiryBiZero.html}, note=[Accessed: 07-August-2025]}