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NAG Toolbox: nag_specfun_bessel_i1_scaled (s18cf)


    1  Purpose
    2  Syntax
    7  Accuracy
    9  Example


nag_specfun_bessel_i1_scaled (s18cf) returns a value of the scaled modified Bessel function e-xI1x via the function name.


[result, ifail] = s18cf(x)
[result, ifail] = nag_specfun_bessel_i1_scaled(x)


nag_specfun_bessel_i1_scaled (s18cf) evaluates an approximation to e-xI1x, where I1 is a modified Bessel function of the first kind. The scaling factor e-x removes most of the variation in I1x.
The function uses the same Chebyshev expansions as nag_specfun_bessel_i1_real (s18af), which returns the unscaled value of I1x.


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.

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

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


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 s18cf_example

fprintf('s18cf example results\n\n');

x = [0  0.5  1   3   6  10  1000  -1];
n = size(x,2);
result = x;

for j=1:n
  [result(j), ifail] = s18cf(x(j));

disp('      x       e^-|x| I_1(x)');
fprintf('%12.3e%12.3e\n',[x; result]);

s18cf example results

      x       e^-|x| I_1(x)
   0.000e+00   0.000e+00
   5.000e-01   1.564e-01
   1.000e+00   2.079e-01
   3.000e+00   1.968e-01
   6.000e+00   1.521e-01
   1.000e+01   1.213e-01
   1.000e+03   1.261e-02
  -1.000e+00  -2.079e-01

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

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