AiryBi
AiryBi[z]
gives the Airy function .
Details
- 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.
- AiryBi can be used with Interval and CenteredInterval objects. »
Examples
open allclose allBasic Examples (5)
Plot over a subset of the reals:
Plot over a subset of the complexes:
Series expansion at the origin:
Series expansion at Infinity:
Scope (40)
Numerical Evaluation (5)
Evaluate numerically to high precision:
The precision of the output tracks the precision of the input:
Evaluate for complex arguments:
Evaluate AiryBi efficiently at high precision:
Compute worst-case guaranteed intervals using Interval and CenteredInterval objects:
Or compute average-case statistical intervals using Around:
Compute the elementwise values of an array:
Or compute the matrix AiryBi function using MatrixFunction:
Specific Values (4)
Visualization (2)
Function Properties (9)
AiryBi is defined for all real and complex values:
Approximate function range of AiryBi:
AiryBi is an analytic function of x:
AiryBi is neither non-increasing nor non-decreasing:
AiryBi is not injective:
AiryBi is not surjective:
AiryBi is neither non-negative nor non-positive:
AiryBi has no singularities or discontinuities:
AiryBi is neither convex nor concave:
Series Expansions (5)
Integral Transforms (2)
Function Identities and Simplifications (3)
Simplify the expression to AiryBi:
FunctionExpand tries to simplify the argument of AiryBi:
Function Representations (4)
Relationship to Bessel functions:
AiryBi can be represented as a DifferentialRoot:
AiryBi can be represented in terms of MeijerG:
TraditionalForm formatting:
Applications (2)
Properties & Relations (5)
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:
Compare with the built-in function AiryBiZero:
Possible Issues (5)
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 for correct parsing in the traditional form:
Text
Wolfram Research (1991), AiryBi, Wolfram Language function, https://reference.wolfram.com/language/ref/AiryBi.html (updated 2022).
CMS
Wolfram Language. 1991. "AiryBi." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2022. https://reference.wolfram.com/language/ref/AiryBi.html.
APA
Wolfram Language. (1991). AiryBi. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/AiryBi.html