NAG Library Function Document

nag_bessel_i0_scaled (s18cec)

+− Contents

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

6 Error Indicators and Warnings

7 Accuracy

8 Parallelism and Performance

9 Further Comments

+− 10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results

1 Purpose

nag_bessel_i0_scaled (s18cec) returns a value of the scaled modified Bessel function

e^{- |x|} I_{0} (x)

2 Specification

#include <nag.h>

#include <nags.h>

double

nag_bessel_i0_scaled (double x)

3 Description

nag_bessel_i0_scaled (s18cec) evaluates an approximation to

e^{- |x|} I_{0} (x)

, where

I_{0}

is a modified Bessel function of the first kind. The scaling factor

e^{- |x|}

removes most of the variation in

I_{0} (x)

The function uses the same Chebyshev expansions as nag_bessel_i0 (s18aec), which returns the unscaled value of

I_{0} (x)

4 References

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

5 Arguments

1: x – doubleInput: On entry: the argument $x$ of the function.

6 Error Indicators and Warnings

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.

8 Parallelism and Performance

Not applicable.

9 Further Comments

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.

NAG Library Function Documentnag_bessel_i0_scaled (s18cec)