NAG FL Interface
s18cef (bessel_​i0_​scaled)

1 Purpose

s18cef returns a value of the scaled modified Bessel function e-xI0x via the function name.

2 Specification

Fortran Interface
Function s18cef ( x, ifail)
Real (Kind=nag_wp) :: s18cef
Integer, Intent (Inout) :: ifail
Real (Kind=nag_wp), Intent (In) :: x
C Header Interface
#include <nag.h>
double  s18cef_ (const double *x, Integer *ifail)
The routine may be called by the names s18cef or nagf_specfun_bessel_i0_scaled.

3 Description

s18cef evaluates an approximation to e-xI0x, where I0 is a modified Bessel function of the first kind. The scaling factor e-x removes most of the variation in I0x.
The routine uses the same Chebyshev expansions as s18aef, which returns the unscaled value of I0x.

4 References

NIST Digital Library of Mathematical Functions

5 Arguments

1: x Real (Kind=nag_wp) Input
On entry: the argument x of the function.
2: ifail Integer Input/Output
On entry: ifail must be set to 0, -1 or 1. If you are unfamiliar with this argument you should refer to Section 4 in the Introduction to the NAG Library FL Interface for details.
For environments where it might be inappropriate to halt program execution when an error is detected, the value -1 or 1 is recommended. If the output of error messages is undesirable, then the value 1 is recommended. Otherwise, if you are not familiar with this argument, the recommended value is 0. When the value -1 or 1 is used it is essential to test the value of ifail on exit.
On exit: ifail=0 unless the routine detects an error or a warning has been flagged (see Section 6).

6 Error Indicators and Warnings

There are no actual failure exits from this routine. ifail is always set to zero. This argument is included for compatibility with other routines in this chapter.

7 Accuracy

Relative errors in the argument are attenuated when propagated into the function value. When the accuracy of the argument is essentially limited by the machine precision, the accuracy of the function value will be similarly limited by at most a small multiple of the machine precision.

8 Parallelism and Performance

s18cef is not threaded in any implementation.

9 Further Comments


10 Example

This example reads values of the argument x from a file, evaluates the function at each value of x and prints the results.

10.1 Program Text

Program Text (s18cefe.f90)

10.2 Program Data

Program Data (s18cefe.d)

10.3 Program Results

Program Results (s18cefe.r)