Evaluates the Airy function of the second kind.

x—Argument for which the function value is desired.

result—The value of the Airy function evaluated at x, Bi(x).

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.

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 (PV-WAVE Advantage), and the BESSJ Function (PV-WAVE Advantage)):

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 (PV-WAVE Advantage)). 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.

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