NAG CL Interface
s18egc (nag_bessel_k_alpha)
1
Purpose
s18egc returns a sequence of values for the modified Bessel functions for real , selected values of and .
2
Specification
void |
s18egc (double x,
Integer ia,
Integer ja,
Integer nl,
double b[],
NagError *fail) |
|
The function may be called by the names: s18egc or nag_bessel_k_alpha.
3
Description
s18egc evaluates a sequence of values for the modified Bessel function of the second kind , where is real and non-negative and is the order. The -member sequence is generated for orders .
4
References
Abramowitz M and Stegun I A (1972) Handbook of Mathematical Functions (3rd Edition) Dover Publications
5
Arguments
-
1:
– double
Input
-
On entry: the argument of the function.
Constraint:
.
-
2:
– Integer
Input
-
3:
– Integer
Input
-
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:
– Integer
Input
-
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:
– double
Output
-
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).
6
Error 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.
7
Accuracy
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.
8
Parallelism and Performance
s18egc is not threaded in any implementation.
None.
10
Example
The example program evaluates and at , and prints the results.
10.1
Program Text
10.2
Program Data
10.3
Program Results