nag_bessel_k_nu_scaled (s18edc) (PDF version)
s Chapter Contents
s Chapter Introduction
NAG C Library Manual

NAG Library Function Document

nag_bessel_k_nu_scaled (s18edc)

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

nag_bessel_k_nu_scaled (s18edc) returns the value of the scaled modified Bessel function e x K ν/4 x  for real x>0 .

2  Specification

#include <nag.h>
#include <nags.h>
double  nag_bessel_k_nu_scaled (double x, Integer nu, NagError *fail)

3  Description

nag_bessel_k_nu_scaled (s18edc) evaluates an approximation to the scaled modified Bessel function of the second kind e x K ν/4 x , where the order ν = -3 , -2 , -1 , 1 , 2  or 3  and x  is real and positive. For negative orders the formula
K - ν / 4 x = K ν/4 x
is used.

4  References

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

5  Arguments

1:     xdoubleInput
On entry: the argument x  of the function.
Constraint: x>0.0 .
2:     nuIntegerInput
On entry: the argument ν  of the function.
Constraint: 1 absnu 3 .
3:     failNagError *Input/Output
The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

NE_INT
On entry, nu=value .
Constraint: 1 absnu 3 .
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.
NE_OVERFLOW_LIKELY
The evaluation has been abandoned due to the likelihood of overflow. The result is returned as zero.
NE_REAL
On entry, x=value .
Constraint: x>0.0 .
NE_TERMINATION_FAILURE
The evaluation has been abandoned due to failure to satisfy the termination condition. The result is returned as zero.
NE_TOTAL_PRECISION_LOSS
The evaluation has been abandoned due to total loss of precision. The result is returned as zero.
NW_SOME_PRECISION_LOSS
The evaluation has been completed but some precision has been lost.

7  Accuracy

All constants in the underlying function are specified to approximately 18 digits of precision. If t  denotes the number of digits of precision in the floating point arithmetic being used, then clearly the maximum number of correct digits in the results obtained is limited by p = mint,18 . Because of errors in argument reduction when computing elementary function inside the underlying function, the actual number of correct digits is limited, in general, by p-s , where s max1, log 10 x  represents the number of digits lost due to the argument reduction. Thus the larger the value of x , the less the precision in the result.

8  Further Comments

None.

9  Example

The example program reads values of the arguments x  and ν  from a file, evaluates the function and prints the results.

9.1  Program Text

Program Text (s18edce.c)

9.2  Program Data

Program Data (s18edce.d)

9.3  Program Results

Program Results (s18edce.r)


nag_bessel_k_nu_scaled (s18edc) (PDF version)
s Chapter Contents
s Chapter Introduction
NAG C Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2012