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Chapter Introduction
NAG Toolbox

NAG Toolbox: nag_specfun_bessel_k0_scaled (s18cc)


    1  Purpose
    2  Syntax
    7  Accuracy
    9  Example


nag_specfun_bessel_k0_scaled (s18cc) returns a value of the scaled modified Bessel function exK0x via the function name.


[result, ifail] = s18cc(x)
[result, ifail] = nag_specfun_bessel_k0_scaled(x)


nag_specfun_bessel_k0_scaled (s18cc) evaluates an approximation to exK0x, where K0 is a modified Bessel function of the second kind. The scaling factor ex removes most of the variation in K0x.
The function uses the same Chebyshev expansions as nag_specfun_bessel_k0_real (s18ac), which returns the unscaled value of K0x.


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


Compulsory Input Parameters

1:     x – double scalar
The argument x of the function.
Constraint: x>0.0.

Optional Input Parameters


Output Parameters

1:     result – double scalar
The result of the function.
2:     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:
On entry, x0.0, K0 is undefined.
On soft failure, nag_specfun_bessel_k0_scaled (s18cc) returns zero.
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 the argument x from a file, evaluates the function at each value of x and prints the results.
function s18cc_example

fprintf('s18cc example results\n\n');

x = [0.4  0.6  1.4  2.5  10  1000];
n = size(x,2);
result = x;

for j=1:n
  [result(j), ifail] = s18cc(x(j));

disp('      x        e^xK_0(x)');
fprintf('%12.3e%12.3e\n',[x; result]);

s18cc example results

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

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

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