nag_bessel_k1_scaled (s18cdc) evaluates an approximation to , where is a modified Bessel function of the second kind. The scaling factor removes most of the variation in .
The function uses the same Chebyshev expansions as nag_bessel_k1 (s18adc), which returns the unscaled value of .
4 References
Abramowitz M and Stegun I A (1972) Handbook of Mathematical Functions (3rd Edition) Dover Publications
5 Arguments
1:
x – doubleInput
On entry: the argument of the function.
Constraint:
.
2:
fail – NagError *Input/Output
The NAG error argument (see Section 3.6 in the Essential Introduction).
6 Error Indicators and Warnings
NE_INTERNAL_ERROR
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
NE_REAL_ARG_LE
On entry, . Constraint: . is undefined and the function returns zero.
NE_REAL_ARG_TOO_SMALL
On entry, . Constraint: . The function returns the value of the function at the smallest permitted value of the argument.
7 Accuracy
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.
8 Parallelism and Performance
Not applicable.
9 Further Comments
None.
10 Example
This example reads values of the argument from a file, evaluates the function at each value of and prints the results.