AIRY_BI Function
Evaluates the Airy function of the second kind.
Usage
result = AIRY_BI(x)
Input Parameters
x—Argument for which the function value is desired.
Returned Value
result—The value of the Airy function evaluated at x, Bi(x).
Input Keywords
Double—If present and nonzero, double precision is used.
Derivative—If present and nonzero, then the derivative of the Airy function of the second kind is computed.
Discussion
The airy function Bi(x) is defined to be:
It can also be expressed in terms of modified Bessel functions of the first kind, Iv(x), and Bessel functions of the first kind Jv(x) (see the BESSI Function, and the BESSJ Function):
and:
Here ε is the machine precision. If x < −1.31ε–2/3, then the answer will have no precision. If x < −1.31ε–1/3, the answer will be less accurate than half precision. In addition, x should not be so large that exp[(2/3)x3/2] overflows.
If the keyword Derivative is set, the airy function Bi'(x) is defined to be the derivative of the Airy function of the second kind, Bi(x) (see the AIRY_BI Function). If x < −1.31ε–2/3, then the answer will have no precision. If x < −1.31ε–1/3, the answer will be less accurate than half precision. Here ε is the machine precision. In addition, x should not be so large that exp[(2/3)x3/2] overflows.
Example
In this example, Bi(–4.9) and Bi'(–4.9) are evaluated.
PRINT, AIRY_BI(-4.9)
; PV-WAVE prints: -0.0577468
PRINT, AIRY_BI(-4.9, /Derivative)
; PV-WAVE prints: 0.827219
