airy
Airy Functions
Description
Examples
Airy Function of Real-Valued x
Define x
.
x = -10:0.01:1;
Calculate Ai(x)
ai = airy(x);
Calculate Bi(x) using .
bi = airy(2,x);
Plot both results together on the same axes.
figure plot(x,ai,'-b',x,bi,'-r') axis([-10 1 -0.6 1.4]) xlabel('x') legend('Ai(x)','Bi(x)','Location','NorthWest')
Airy Function of Complex-Valued x
Compute the Airy function at a slice through the complex plane at .
Take a slice through the complex plane.
x = -4:0.1:4; z = x+1i;
Calculate Ai(z).
w = airy(z);
Plot the real part of the result.
figure
plot(x, real(w))
axis([-4 4 -1.5 1])
xlabel('real(z)')
Scaled Airy Function
Define x
.
x = -10:0.01:1;
Calculate the scaled and unscaled Airy function.
scaledAi = airy(0,x,1); noscaleAi = airy(0,x,0);
Plot the real part of each result.
rscaled = real(scaledAi); rnoscale = real(noscaleAi); figure plot(x,rscaled,'-b',x,rnoscale,'-r') axis([-10 1 -0.60 0.60]) xlabel('x') legend('scaled','not scaled','Location','SouthEast')
Input Arguments
Z
— System variable
vector | matrix | N-D Array
System variable, specified as a real or complex vector, matrix, or N-D array.
Data Types: single
| double
Complex Number Support: Yes
k
— Type of Airy function
0
(default) | 1
| 2
| 3
Type of Airy function, specified as one of four values.
k | Returns |
---|---|
| Airy function,,
which is the same as |
| First derivative of Airy function, . |
| Airy function of the second kind, |
| First derivative of Airy function of the second kind, |
Data Types: single
| double
scale
— Scaling option
0
(default) | 1
Scaling option, specified as 0
or 1
.
Use scale = 1
to enable the scaling of Z
.
The values you specify for k
and scale
determine
the scaling function airy
applies to Z
.
scale | k | Scaling applied to output |
---|---|---|
0 | Any | None |
1 | 0 or 1 |
|
1 | 2 or 3 |
|
Data Types: single
| double
Output Arguments
W
— Airy function of Z
vector | matrix | N-D Array
Airy function of Z
, returned as an array
the same size as Z
.
More About
Airy Functions
The Airy functions form a pair of linearly independent solutions to
The relationship between the Airy and modified Bessel functions is
where
Extended Capabilities
C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.
Usage notes and limitations:
Always returns a complex result.
Strict single-precision calculations are not supported. In the generated code, single-precision inputs produce single-precision outputs. However, variables inside the function might be double-precision.
Thread-Based Environment
Run code in the background using MATLAB® backgroundPool
or accelerate code with Parallel Computing Toolbox™ ThreadPool
.
This function fully supports thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.
Version History
Introduced before R2006a
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