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NAG Library Routine Document

s18cff (bessel_i1_scaled)

▸▿ 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

s18cff returns a value of the scaled modified Bessel function

e^{- |x|} I_{1} (x)

via the routine name.

2

Specification

Fortran Interface

Function s18cff (

x, ifail)

Real (Kind=nag_wp)	::	s18cff
Integer, Intent (Inout)	::	ifail
Real (Kind=nag_wp), Intent (In)	::	x

C Header Interface

#include nagmk26.h

double

s18cff_ ( const double *x, Integer *ifail)

3

Description

s18cff evaluates an approximation to

e^{- |x|} I_{1} (x)

, where

I_{1}

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

e^{- |x|}

removes most of the variation in

I_{1} (x)

The routine uses the same Chebyshev expansions as s18aff, which returns the unscaled value of

I_{1} (x)

4

References

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

5

Arguments

1: $x$ – Real (Kind=nag_wp)Input: On entry: the argument $x$ of the function.
2: $ifail$ – IntegerInput/Output: On entry: ifail must be set to $0$ , $- 1 or 1$ . If you are unfamiliar with this argument you should refer to Section 3.4 in How to Use the NAG Library and its Documentation for details.
For environments where it might be inappropriate to halt program execution when an error is detected, the value $- 1 or 1$ is recommended. If the output of error messages is undesirable, then the value $1$ is recommended. Otherwise, if you are not familiar with this argument, the recommended value is $0$ . When the value $- 1 or 1$ is used it is essential to test the value of ifail on exit.

On exit: $ifail = 0$ unless the routine detects an error or a warning has been flagged (see Section 6).

6

Error Indicators and Warnings

There are no actual failure exits from this routine. ifail is always set to zero. This argument is included for compatibility with other routines in this chapter.

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

s18cff is not threaded in any implementation.

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 Routine Document

s18cff (bessel_i1_scaled)

▸▿ 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