# NAG FL Interfaces18cef (bessel_​i0_​scaled)

## ▸▿ Contents

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## 1Purpose

s18cef returns a value of the scaled modified Bessel function ${e}^{-|x|}{I}_{0}\left(x\right)$ via the function name.

## 2Specification

Fortran Interface
 Function s18cef ( x,
 Real (Kind=nag_wp) :: s18cef Integer, Intent (Inout) :: ifail Real (Kind=nag_wp), Intent (In) :: x
#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.

## 3Description

s18cef evaluates an approximation to ${e}^{-|x|}{I}_{0}\left(x\right)$, where ${I}_{0}$ is a modified Bessel function of the first kind. The scaling factor ${e}^{-|x|}$ removes most of the variation in ${I}_{0}\left(x\right)$.
The routine uses the same Chebyshev expansions as s18aef, which returns the unscaled value of ${I}_{0}\left(x\right)$.
NIST Digital Library of Mathematical Functions

## 5Arguments

1: $\mathbf{x}$Real (Kind=nag_wp) Input
On entry: the argument $x$ of the function.
2: $\mathbf{ifail}$Integer Input/Output
There are no failure exits from this routine. The argument ifail is included for consistency with other routines in this chapter.

None.

## 7Accuracy

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.

## 8Parallelism and Performance

s18cef is not threaded in any implementation.

None.

## 10Example

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

### 10.1Program Text

Program Text (s18cefe.f90)

### 10.2Program Data

Program Data (s18cefe.d)

### 10.3Program Results

Program Results (s18cefe.r)