airy (MATLAB Function Reference)

Airy functions

Syntax

W = airy(Z) 
W = airy(k,Z) 
[W,ierr] = airy(k,Z)

Definition

The Airy functions form a pair of linearly independent solutions to:

The relationship between the Airy and modified Bessel functions is:

where

,

Description

W = airy(Z) returns the Airy function, Ai(Z), for each element of the complex array Z.

W = airy(k,Z) returns different results depending on the value of k:

k
Returns

0
The same result as airy(Z).

1
The derivative, .

2
The Airy function of the second kind, .

3
The derivative, .

k	Returns
`0`	The same result as `airy(Z)`.
`1`	The derivative, .
`2`	The Airy function of the second kind, .
`3`	The derivative, .

[W,ierr] = airy(k,Z) also returns an array of error flags.

ierr = 1

Illegal arguments.

ierr = 2

Overflow. Return Inf.

ierr = 3

Some loss of accuracy in argument reduction.

ierr = 4

Unacceptable loss of accuracy, Z too large.

ierr = 5

No convergence. Return NaN.

`ierr = 1`	Illegal arguments.
`ierr = 2`	Overflow. Return `Inf`.
`ierr = 3`	Some loss of accuracy in argument reduction.
`ierr = 4`	Unacceptable loss of accuracy, `Z` too large.
`ierr = 5`	No convergence. Return `NaN`.

See Also

besseli, besselj, besselk, bessely

References

[1] Amos, D. E., "A Subroutine Package for Bessel Functions of a Complex Argument and Nonnegative Order," Sandia National Laboratory Report, SAND85-1018, May, 1985.

[2] Amos, D. E., "A Portable Package for Bessel Functions of a Complex Argument and Nonnegative Order," Trans. Math. Software, 1986.

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