NAG Library Function Document
nag_bessel_k1 (s18adc) returns the value of the modified Bessel function, .
||nag_bessel_k1 (double x,
nag_bessel_k1 (s18adc) evaluates an approximation to the modified Bessel function of the second kind, .
The function is based on Chebyshev expansions.
For near zero, . For very small on some machines, it is impossible to calculate without overflow and the function must fail.
Abramowitz M and Stegun I A (1972) Handbook of Mathematical Functions (3rd Edition) Dover Publications
x – doubleInput
On entry: the argument of the function.
fail – NagError *Input/Output
The NAG error argument (see Section 3.6
in the Essential Introduction).
6 Error Indicators and Warnings
On entry, x
must not be less than or equal to 0.0:
is undefined and the function returns zero.
On entry, x
must be greater than
is too small, there is a danger of overflow and the function returns approximately the largest representable value.
Let and be the relative errors in the argument and result respectively.
If is somewhat larger than the machine precision (i.e., if is due to data errors etc. ), then and are approximately related by .
However, if is of the same order as the machine precision, then rounding errors could make slightly larger than the above relation predicts.
For small , and there is no amplification of errors.
For large , and we have strong amplification of the relative error. Eventually , which is asymptotically given by , becomes so small that it cannot be calculated without underflow and hence the function will return zero. Note that for large the errors will be dominated by those of the math library function exp.
The following program reads values of the argument from a file, evaluates the function at each value of and prints the results.
9.1 Program Text
Program Text (s18adce.c)
9.2 Program Data
Program Data (s18adce.d)
9.3 Program Results
Program Results (s18adce.r)