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IMSL_AIRY_BI

IMSL_AIRY_BI

IMSL_AIRY_BI

The IMSL_AIRY_BI function evaluates the Airy function of the second kind.

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 IMSL_BESSI, and IMSL_BESSJ):

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 IMSL_AIRY_BI). 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.



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