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Chapter Contents
Chapter Introduction
NAG Toolbox

NAG Toolbox: nag_specfun_bessel_k0_scaled_vector (s18cq)


    1  Purpose
    2  Syntax
    7  Accuracy
    9  Example


nag_specfun_bessel_k0_scaled_vector (s18cq) returns an array of values of the scaled modified Bessel function exK0x.


[f, ivalid, ifail] = s18cq(x, 'n', n)
[f, ivalid, ifail] = nag_specfun_bessel_k0_scaled_vector(x, 'n', n)


nag_specfun_bessel_k0_scaled_vector (s18cq) evaluates an approximation to exiK0xi, where K0 is a modified Bessel function of the second kind for an array of arguments xi, for i=1,2,,n. The scaling factor ex removes most of the variation in K0x.
The function uses the same Chebyshev expansions as nag_specfun_bessel_k0_real_vector (s18aq), which returns an array of the unscaled values of K0x.


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


Compulsory Input Parameters

1:     xn – double array
The argument xi of the function, for i=1,2,,n.
Constraint: xi>0.0, for i=1,2,,n.

Optional Input Parameters

1:     n int64int32nag_int scalar
Default: the dimension of the array x.
n, the number of points.
Constraint: n0.

Output Parameters

1:     fn – double array
exiK0xi, the function values.
2:     ivalidn int64int32nag_int array
ivalidi contains the error code for xi, for i=1,2,,n.
No error.
On entry,xi0.0, K0xi is undefined. fi contains 0.0.
3:     ifail int64int32nag_int scalar
ifail=0 unless the function detects an error (see Error Indicators and Warnings).

Error Indicators and Warnings

Errors or warnings detected by the function:

Cases prefixed with W are classified as warnings and do not generate an error of type NAG:error_n. See nag_issue_warnings.

W  ifail=1
On entry, at least one value of x was invalid.
Check ivalid for more information.
Constraint: n0.
An unexpected error has been triggered by this routine. Please contact NAG.
Your licence key may have expired or may not have been installed correctly.
Dynamic memory allocation failed.


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.

Further Comments



This example reads values of x from a file, evaluates the function at each value of xi and prints the results.
function s18cq_example

fprintf('s18cq example results\n\n');

x = [0.4; 0.6; 1.4; 2.5; 10; 1000];

[f, ivalid, ifail] = s18cq(x);

fprintf('     x         e^xK_0(x)   ivalid\n');
for i=1:numel(x)
  fprintf('%12.3e%12.3e%5d\n', x(i), f(i), ivalid(i));

s18cq example results

     x         e^xK_0(x)   ivalid
   4.000e-01   1.663e+00    0
   6.000e-01   1.417e+00    0
   1.400e+00   9.881e-01    0
   2.500e+00   7.595e-01    0
   1.000e+01   3.916e-01    0
   1.000e+03   3.963e-02    0

PDF version (NAG web site, 64-bit version, 64-bit version)
Chapter Contents
Chapter Introduction
NAG Toolbox

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