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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