BI

This function evaluates the Airy function of the second kind.

Function Return Value

BI — Function value. (Output)

Required Arguments

X — Argument for which the Airy function value is desired. (Input)

FORTRAN 90 Interface

Generic: BI (X)

Specific: The specific interface names are S_BI and D_BI.

FORTRAN 77 Interface

Single: BI (X)

Double: The double precision name is DBI.

Description

The Airy function of the second kind 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 BSIS and BSJS):

and

Let ɛ = AMACH(4), the machine precision. If

, then the answer will have no precision. If

, the answer will be less accurate than half precision. In addition, x should not be so large that

overflows. If overflows are a problem, consider using the exponentially scaled form of the Airy function of the second kind, BIE, instead.

Example

In this example, Bi(–4.9) is computed and printed.

USE BI_INT

USE UMACH_INT

IMPLICIT NONE

! Declare variables

INTEGER NOUT

REAL VALUE, X

! Compute

X = -4.9

VALUE = BI(X)

! Print the results

CALL UMACH (2, NOUT)

WRITE (NOUT,99999) X, VALUE

99999 FORMAT (' BI(', F6.3, ') = ', F6.3)

END

Output

BI(-4.900) = -0.058