1: $z$ – Complex Input: On entry: the argument $z$ of the function.

Constraint: $z \neq (0.0, 0.0)$ when $nl < 0$ .
2: $a$ – double Input: On entry: the order $α$ of the first member in the required sequence of function values.

Constraint: $0.0 \leq a < 1.0$ .
3: $nl$ – Integer Input: On entry: the value of $N$ .

Constraint: $abs (nl) \leq 101$ .
4: $b [abs (nl) + 1]$ – Complex Output: On exit: with $fail . code =$ NE_NOERROR or NW_SOME_PRECISION_LOSS, the required sequence of function values: $b [n - 1]$ contains $J_{α + n - 1} (z)$ if $nl \geq 0$ and $J_{α - n + 1} (z)$ otherwise, for $n = 1, 2, \dots, abs (nl) + 1$ .
5: $fail$ – 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_ALLOC_FAIL: Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
NE_BAD_PARAM: On entry, argument $⟨ value ⟩$ had an illegal value.
NE_INT: On entry, $| nl | = ⟨ value ⟩$ .
Constraint: $| nl | \leq 101$ .

On entry, $nl = ⟨ value ⟩$ .
Constraint: when $nl < 0$ , $z \neq (0.0, 0.0)$ .
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.
See Section 7.5 in the Introduction to the NAG Library CL Interface for further information.
NE_NO_LICENCE: Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library CL Interface for further information.
NE_OVERFLOW_LIKELY: Computation abandoned due to the likelihood of overflow.
NE_REAL: On entry, $a = ⟨ value ⟩$ .
Constraint: $a < 1.0$ .

On entry, $a = ⟨ value ⟩$ .
Constraint: $a \geq 0.0$ .
NE_TERMINATION_FAILURE: Computation abandoned due to failure to satisfy the termination condition.
NE_TOTAL_PRECISION_LOSS: Computation abandoned due to total loss of precision.
NW_SOME_PRECISION_LOSS: Computation completed but some precision has been lost.

7 Accuracy

All constants in s17dcc and s17dec are specified to approximately

18

digits of precision. If

t

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

p = \min (t, 18)

. Because of errors in argument reduction when computing elementary functions inside s17dcc and s17dec, the actual number of correct digits is limited, in general, by

p - s

, where

s \approx \max (1, | \log_{10} | z | |, | \log_{10} | α | |)

represents the number of digits lost due to the argument reduction. Thus the larger the values of

| z |

and

| α |

, the less the precision in the result.

8 Parallelism and Performance

s18gkc is not threaded in any implementation.

9 Further Comments

None.

10 Example

This example evaluates

J_{0} (z), J_{1} (z), J_{2} (z)

and

J_{3} (z)

z = 0.6 - 0.8 i

, and prints the results.

s18gk: FL CL CPP AD

NAG CL Interfaces18gkc (bessel_​j_​seq_​complex)

▸▿ Contents

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

6 Error Indicators and Warnings

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results

NAG CL Interface
s18gkc (bessel_j_seq_complex)