# NAG Library Function Document

## 1Purpose

nag_bessel_i1_scaled (s18cfc) returns a value of the scaled modified Bessel function ${e}^{-\left|x\right|}{I}_{1}\left(x\right)$.

## 2Specification

 #include #include
 double nag_bessel_i1_scaled (double x)

## 3Description

nag_bessel_i1_scaled (s18cfc) 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 function uses the same Chebyshev expansions as nag_bessel_i1 (s18afc), 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:    $\mathbf{x}$doubleInput
On entry: the argument $x$ of the function.

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

nag_bessel_i1_scaled (s18cfc) 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 (s18cfce.c)

### 10.2Program Data

Program Data (s18cfce.d)

### 10.3Program Results

Program Results (s18cfce.r)

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