# airy (MathScript RT Module Function)

LabVIEW 2012 MathScript RT Module Help

Edition Date: June 2012

Part Number: 373123C-01

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Requires: MathScript RT Module

## Syntax

y = airy(x)

y = airy(kind, x)

[y, error] = airy(x)

[y, error] = airy(kind, x)

## Description

Computes the Airy functions Ai and Bi as well as their derivatives.

Details

Examples

## Inputs

Name Description
x Specifies a real or complex scalar, vector, or matrix.
kind Specifies the kind of Airy function to evaluate. kind is an integer that accepts the following values.

 0 Computes the Airy function of the first kind, Ai(x). 1 Computes the derivative of the Airy function of the first kind, Ai'(x). 2 Computes the Airy function of the second kind, Bi(x). 3 Computes the derivative of the Airy function of the second kind, Bi'(x).

## Outputs

Name Description
y Returns an Airy function or the derivative of an Airy function. y is a matrix of the same size as x.
error Returns error information about the evaluation of the Airy functions. error is a matrix of integers in which each element can return the following values.

 0 Indicates that no error occurred. 1 Indicates that you specified invalid inputs. 2 Indicates that the result is too large for the data type of y. 3 Indicates that LabVIEW achieved less than half the machine accuracy in the calculation because |x| is greater than approximately 1.3E8. 4 Indicates that the result is meaningless because |x| is greater than approximately 1.8E16. 5 Indicates that the calculation did not reach the termination condition so LabVIEW did not complete the calculation.

## Details

Ai(x) and Bi(x) solve the following equation: w'' - x*w = 0.
LabVIEW computes Ai(x) using the following equation: Ai(x) = sqrt(x/3)*bessel_k(1/3, (2*sqrt(x)3)/3). LabVIEW computes Bi(x) using a similar equation.

The following table lists the support characteristics of this function.

 Supported in the LabVIEW Run-Time Engine Yes Supported on RT targets Yes Suitable for bounded execution times on RT Not characterized

X = [0:0.01:2];
AI = airy(X);
plot(X, AI)