NAG FL Interface
s18cef (bessel_​i0_​scaled)

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1 Purpose

s18cef returns a value of the scaled modified Bessel function e-|x|I0(x) 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-|x|I0(x), where I0 is a modified Bessel function of the first kind. The scaling factor e-|x| removes most of the variation in I0(x).
The routine uses the same Chebyshev expansions as s18aef, which returns the unscaled value of I0(x).

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
There are no failure exits from this routine. The argument ifail is included for consistency with other routines in this chapter.

6 Error Indicators and Warnings


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

Background information to multithreading can be found in the Multithreading documentation.
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)