1: $x$ – double Input: On entry: the argument $x$ of the function.

Constraint: if $nl < 0$ , $x \neq 0.0$ .
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: $b [\times]$ – Complex Output: On exit: with $fail . code = NE_NOERROR$ or $fail . code = NW_SOME_PRECISION_LOSS$ , the required sequence of function values: b $(n)$ contains $J_{α + n - 1} (x)$ if $nl \geq 0$ and $J_{α - n + 1} (x)$ 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_INT: On entry, $nl = ⟨ value ⟩$ .
Constraint: $abs (nl) \leq 101$ .
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, $a = ⟨ value ⟩$ .
Constraint: $0.0 \leq a < 1.0$ .
NE_REAL_INT: On entry, $x = ⟨ value ⟩$ , $nl = ⟨ value ⟩$ .
Constraint: $x \neq 0.0$ when $nl < 0$ .
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 functions are 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 the underlying functions are, the actual number of correct digits is limited, in general, by

p - s

, where

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

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

| x |

and

| α |

, the less the precision in the result.

8 Parallelism and Performance

s18ekc is not threaded in any implementation.

9 Further Comments

None.

10 Example

The example program evaluates

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

and

J_{3} (x)

x = 0.5

, and prints the results.

s18ek: FL CL CPP AD

NAG CL Interfaces18ekc (nag_bessel_j_alpha)

▸▿ 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
s18ekc (nag_bessel_j_alpha)