NAG Library Function Document
nag_kelvin_kei (s19adc) returns a value for the Kelvin function .
||nag_kelvin_kei (double x,
nag_kelvin_kei (s19adc) evaluates an approximation to the Kelvin function .
The function is based on several Chebyshev expansions.
For large , is so small that it cannot be computed without underflow and the function fails.
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
is too large, and the result underflows and the function returns zero.
On entry, x
must not be less than 0.0:
The function is undefined and returns zero.
Let be the absolute error in the result, and be the relative error in the argument. If is somewhat larger than the machine representation error, then we have .
For small , errors are attenuated by the function and hence are limited by the machine precision.
For medium and large , the error behaviour, like the function itself, is oscillatory and hence only absolute accuracy of the function can be maintained. For this range of , the amplitude of the absolute error decays like , which implies a strong attenuation of error. Eventually, , which is asymptotically given by , becomes so small that it cannot be calculated without causing underflow and therefore the function returns zero. Note that for large , the errors are dominated by those of the math library function exp.
Underflow may occur for a few values of
close to the zeros of
, which causes failure NE_REAL_ARG_GT
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 (s19adce.c)
9.2 Program Data
Program Data (s19adce.d)
9.3 Program Results
Program Results (s19adce.r)