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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.

Example

n this example, Bi(-4.9) and Bi′(-4.9) are evaluated.

`PRINT, IMSL_AIRY_BI(-4.9)`
`  -0.0577468`
`PRINT, IMSL_AIRY_BI(-4.9, /Derivative)`
`  0.827219`

Syntax

Result = IMSL_AIRY_BI(X [, DERIVATIVE=value] [, /DOUBLE])

Return Value

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

Arguments

X

Argument for which the function value is desired.

Keywords

DERIVATIVE (optional)

If present and nonzero, then the derivative of the Airy function is computed.

DOUBLE (optional)

If present and nonzero, double precision is used.

Version History

 6.4 Introduced