NAG Library Function Document
nag_kelvin_bei (s19abc) returns a value for the Kelvin function .
||nag_kelvin_bei (double x,
nag_kelvin_bei (s19abc) evaluates an approximation to the Kelvin function .
The function is based on several Chebyshev expansions.
For large , there is a danger of the result being totally inaccurate, as the error amplification factor grows in an essentially exponential manner; therefore 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, .
is too large for an accurate result to be returned and the function returns zero.
Since the function is oscillatory, the absolute error rather than the relative error is important. Let be the absolute error in the function, and be the relative error in the argument. If is somewhat larger than the machine precision, then we have (provided is within machine bounds).
For small the error amplification is insignificant and thus the absolute error is effectively bounded by the machine precision.
For medium and large , the error behaviour is oscillatory and its amplitude grows like . Therefore it is impossible to calculate the functions with any accuracy when . Note that this value of is much smaller than the minimum value of for which the function overflows.
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 (s19abce.c)
9.2 Program Data
Program Data (s19abce.d)
9.3 Program Results
Program Results (s19abce.r)