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NAG C Library Manual

NAG Library Function Documentnag_bessel_k0_scaled_vector (s18cqc)

1  Purpose

nag_bessel_k0_scaled_vector (s18cqc) returns an array of values of the scaled modified Bessel function ${e}^{x}{K}_{0}\left(x\right)$.

2  Specification

 #include #include
 void nag_bessel_k0_scaled_vector (Integer n, const double x[], double f[], Integer ivalid[], NagError *fail)

3  Description

nag_bessel_k0_scaled_vector (s18cqc) evaluates an approximation to ${e}^{{x}_{i}}{K}_{0}\left({x}_{i}\right)$, where ${K}_{0}$ is a modified Bessel function of the second kind for an array of arguments ${x}_{\mathit{i}}$, for $\mathit{i}=1,2,\dots ,n$. 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_vector (s18aqc), which returns an array of the unscaled values 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:     nIntegerInput
On entry: $n$, the number of points.
Constraint: ${\mathbf{n}}\ge 0$.
2:     x[n]const doubleInput
On entry: the argument ${x}_{\mathit{i}}$ of the function, for $\mathit{i}=1,2,\dots ,{\mathbf{n}}$.
Constraint: ${\mathbf{x}}\left[\mathit{i}-1\right]>0.0$, for $\mathit{i}=1,2,\dots ,{\mathbf{n}}$.
3:     f[n]doubleOutput
On exit: ${e}^{{x}_{i}}{K}_{0}\left({x}_{i}\right)$, the function values.
4:     ivalid[n]IntegerOutput
On exit: ${\mathbf{ivalid}}\left[\mathit{i}-1\right]$ contains the error code for ${x}_{\mathit{i}}$, for $\mathit{i}=1,2,\dots ,{\mathbf{n}}$.
${\mathbf{ivalid}}\left[i-1\right]=0$
No error.
${\mathbf{ivalid}}\left[i-1\right]=1$
 On entry, ${x}_{i}\le 0.0$, ${K}_{0}\left({x}_{i}\right)$ is undefined. ${\mathbf{f}}\left[\mathit{i}-1\right]$ contains $0.0$.
5:     failNagError *Input/Output
The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

On entry, argument $〈\mathit{\text{value}}〉$ had an illegal value.
NE_INT
On entry, ${\mathbf{n}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{n}}\ge 0$.
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.
NW_IVALID
On entry, at least one value of x was invalid.

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.

None.

9  Example

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

9.1  Program Text

Program Text (s18cqce.c)

9.2  Program Data

Program Data (s18cqce.d)

9.3  Program Results

Program Results (s18cqce.r)