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NAG Library Manual

# NAG Library Function Documentnag_bessel_k0_scaled (s18ccc)

## 1  Purpose

nag_bessel_k0_scaled (s18ccc) returns a value of the scaled modified Bessel function ${e}^{x}{K}_{0}\left(x\right)$.

## 2  Specification

 #include #include
 double nag_bessel_k0_scaled (double x, NagError *fail)

## 3  Description

nag_bessel_k0_scaled (s18ccc) evaluates an approximation to ${e}^{x}{K}_{0}\left(x\right)$, where ${K}_{0}$ is a modified Bessel function of the second kind. The scaling factor ${e}^{x}$ removes most of the variation in ${K}_{0}\left(x\right)$.
The function uses the same Chebyshev expansions as nag_bessel_k0 (s18acc), which returns the unscaled value of ${K}_{0}\left(x\right)$.

## 4  References

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.
Constraint: ${\mathbf{x}}>0.0$.
2:    $\mathbf{fail}$NagError *Input/Output
The NAG error argument (see Section 2.7 in How to Use the NAG Library and its Documentation).

## 6  Error Indicators and Warnings

NE_ALLOC_FAIL
Dynamic memory allocation failed.
See Section 2.3.1.2 in How to Use the NAG Library and its Documentation for further information.
NE_INTERNAL_ERROR
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
An unexpected error has been triggered by this function. Please contact NAG.
See Section 2.7.6 in How to Use the NAG Library and its Documentation for further information.
NE_NO_LICENCE
Your licence key may have expired or may not have been installed correctly.
See Section 2.7.5 in How to Use the NAG Library and its Documentation for further information.
NE_REAL_ARG_LE
On entry, ${\mathbf{x}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{x}}>0.0$.

## 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

nag_bessel_k0_scaled (s18ccc) is not threaded in any implementation.

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 (s18ccce.c)

### 10.2  Program Data

Program Data (s18ccce.d)

### 10.3  Program Results

Program Results (s18ccce.r)