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NAG Library Manual

# NAG Library Function Documentnag_bessel_i0_scaled (s18cec)

## 1  Purpose

nag_bessel_i0_scaled (s18cec) returns a value of the scaled modified Bessel function ${e}^{-\left|x\right|}{I}_{0}\left(x\right)$.

## 2  Specification

 #include #include
 double nag_bessel_i0_scaled (double x)

## 3  Description

nag_bessel_i0_scaled (s18cec) evaluates an approximation to ${e}^{-\left|x\right|}{I}_{0}\left(x\right)$, where ${I}_{0}$ is a modified Bessel function of the first kind. The scaling factor ${e}^{-\left|x\right|}$ removes most of the variation in ${I}_{0}\left(x\right)$.
The function uses the same Chebyshev expansions as nag_bessel_i0 (s18aec), which returns the unscaled value of ${I}_{0}\left(x\right)$.
Abramowitz M and Stegun I A (1972) Handbook of Mathematical Functions (3rd Edition) Dover Publications

## 5  Arguments

1:    $\mathbf{x}$doubleInput
On entry: the argument $x$ of the function.

None.

## 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.

Not applicable.

None.

## 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 (s18cece.c)

### 10.2  Program Data

Program Data (s18cece.d)

### 10.3  Program Results

Program Results (s18cece.r)