The function may be called by the names: s18ehc or nag_bessel_k_alpha_scaled.
3Description
s18ehc evaluates a sequence of values for the scaled modified Bessel function of the second kind , where is real and non-negative and is the order. The -member sequence is generated for orders .
4References
Abramowitz M and Stegun I A (1972) Handbook of Mathematical Functions (3rd Edition) Dover Publications
5Arguments
1: – doubleInput
On entry: the argument of the function.
Constraint:
.
2: – IntegerInput
3: – IntegerInput
On entry: the numerator and denominator , respectively, of the order of the first member in the required sequence of function values. Only the following combinations of pairs of values of and are allowed:
and corresponds to ;
and corresponds to ;
and corresponds to ;
and corresponds to ;
and corresponds to ;
and corresponds to .
Constraint:
ia and ja must constitute a valid pair , , , , or .
4: – IntegerInput
On entry: the value of . Note that the order of the last member in the required sequence of function values is given by .
Constraint:
.
5: – doubleOutput
On exit: with or , the required sequence of function values: b contains , for .
6: – NagError *Input/Output
The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).
6Error Indicators and Warnings
NE_INT
On entry, .
Constraint: .
NE_INT_2
On entry, , .
Constraint: ia and ja must constitute a valid pair (ia,ja).
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_OVERFLOW_LIKELY
The evaluation has been abandoned due to the likelihood of overflow.
NE_REAL
On entry, .
Constraint: .
NE_TERMINATION_FAILURE
The evaluation has been abandoned due to failure to satisfy the termination condition.
NE_TOTAL_PRECISION_LOSS
The evaluation has been abandoned due to total loss of precision.
NW_SOME_PRECISION_LOSS
The evaluation has been completed but some precision has been lost.
7Accuracy
All constants in the underlying function are specified to approximately 18 digits of precision. If denotes the number of digits of precision in the floating-point arithmetic being used, then clearly the maximum number of correct digits in the results obtained is limited by . Because of errors in argument reduction when computing elementary functions inside the underlying function, the actual number of correct digits is limited, in general, by , where represents the number of digits lost due to the argument reduction. Thus the larger the value of , the less the precision in the result.
8Parallelism and Performance
Background information to multithreading can be found in the Multithreading documentation.
s18ehc is not threaded in any implementation.
9Further Comments
None.
10Example
The example program evaluates and at , and prints the results.