# NAG Library Routine Document

## 1Purpose

s18cff returns a value of the scaled modified Bessel function ${e}^{-\left|x\right|}{I}_{1}\left(x\right)$ via the routine name.

## 2Specification

Fortran Interface
 Function s18cff ( x,
 Real (Kind=nag_wp) :: s18cff Integer, Intent (Inout) :: ifail Real (Kind=nag_wp), Intent (In) :: x
#include nagmk26.h
 double s18cff_ (const double *x, Integer *ifail)

## 3Description

s18cff evaluates an approximation to ${e}^{-\left|x\right|}{I}_{1}\left(x\right)$, where ${I}_{1}$ is a modified Bessel function of the first kind. The scaling factor ${e}^{-\left|x\right|}$ removes most of the variation in ${I}_{1}\left(x\right)$.
The routine uses the same Chebyshev expansions as s18aff, which returns the unscaled value of ${I}_{1}\left(x\right)$.

## 4References

Abramowitz M and Stegun I A (1972) Handbook of Mathematical Functions (3rd Edition) Dover Publications

## 5Arguments

1:     $\mathbf{x}$ – Real (Kind=nag_wp)Input
On entry: the argument $x$ of the function.
2:     $\mathbf{ifail}$ – IntegerInput/Output
On entry: ifail must be set to $0$, $-1\text{​ or ​}1$. If you are unfamiliar with this argument you should refer to Section 3.4 in How to Use the NAG Library and its Documentation for details.
For environments where it might be inappropriate to halt program execution when an error is detected, the value $-1\text{​ or ​}1$ 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 $-\mathbf{1}\text{​ or ​}\mathbf{1}$ is used it is essential to test the value of ifail on exit.
On exit: ${\mathbf{ifail}}={\mathbf{0}}$ unless the routine detects an error or a warning has been flagged (see Section 6).

## 6Error 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.

## 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

s18cff 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 (s18cffe.f90)

### 10.2Program Data

Program Data (s18cffe.d)

### 10.3Program Results

Program Results (s18cffe.r)

© The Numerical Algorithms Group Ltd, Oxford, UK. 2017