NAG Library Function Document
nag_bessel_i0 (s18aec) returns the value of the modified Bessel function .
||nag_bessel_i0 (double x,
nag_bessel_i0 (s18aec) evaluates an approximation to the modified Bessel function of the first kind, .
The function is based on Chebyshev expansions.
For large , the function must fail because of the danger of overflow in calculating .
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 and the function returns the approximate value of at the nearest valid argument.
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 machine precision, then rounding errors could make slightly larger than the above relation predicts.
For small the amplification factor is approximately , which implies strong attenuation of the error, but in general can never be less than the machine precision.
For large , and we have strong amplification of errors. However, the function must fail for quite moderate values of , because would overflow; hence in practice the loss of accuracy for large is not excessive. 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 (s18aece.c)
9.2 Program Data
Program Data (s18aece.d)
9.3 Program Results
Program Results (s18aece.r)