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

Constraint: $x > 0.0$ .
2: $n$ – Integer Input: On entry: the index of the first member $n$ of the sequence of functions.

Constraint: $n \geq 0$ .
3: $m$ – Integer Input: On entry: the number of members $m$ required in the sequence $w (k, x)$ , for $k = n, \dots, n + m - 1$ .

Constraint: $m \geq 1$ .
4: $ans [m]$ – double Output: On exit: the first $m$ elements of ans contain the required values $w (k, x)$ , for $k = n, \dots, n + m - 1$ .
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, $m = ⟨ value ⟩$ .
Constraint: $m \geq 1$ .

On entry, $n = ⟨ value ⟩$ .
Constraint: $n \geq 0$ .
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_INTERNAL_WORKSPACE: There is not enough internal workspace to continue computation. m is probably too large.
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, $x = ⟨ value ⟩$ .
Constraint: $x > 0.0$ .
NE_UNDERFLOW_LIKELY: Computation abandoned due to the likelihood of underflow.

7 Accuracy

All constants in s14adc are given to approximately

18

digits of precision. Calling the number of digits of precision in the floating-point arithmetic being used

t

, then clearly the maximum number of correct digits in the results obtained is limited by

p = \min (t, 18)

. Empirical tests of s14adc, taking values of

x

in the range

0.0 < x < 50.0

, and

n

in the range

1 \leq n \leq 50

, have shown that the maximum relative error is a loss of approximately two decimal places of precision. Tests with

n = 0

, i.e., testing the function

- ψ (x)

, have shown somewhat better accuracy, except at points close to the zero of

ψ (x)

x ≃ 1.461632

, where only absolute accuracy can be obtained.

s14adc is not threaded in any implementation.

The time taken for a call of s14adc is approximately proportional to

m

, plus a constant. In general, it is much cheaper to call s14adc with

m

greater than

1

to evaluate the function

w (k, x)

, for

k = n, \dots, n + m - 1

, rather than to make

m

separate calls of s14adc.

This example reads values of the argument

x

from a file, evaluates the function at each value of

x

and prints the results.

s14ad: FL CL CPP AD