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Airy functions

Syntax

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, .

[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.

See Also

besseli     Modified Bessel functions of the first kind

besselj     Bessel functions of the first kind

besselk     Modified Bessel functions of the third kind

bessely     Bessel functions of the second kind

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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