Kölbig K S (1972) Programs for computing the logarithm of the gamma function, and the digamma function, for complex arguments Comp. Phys. Comm. 4 221–226

5 Arguments

1: $z$ – Complex (Kind=nag_wp) Input: On entry: the argument $z$ of the function.

Constraint: $Re (z)$ must not be ‘too close’ (see Section 6) to a non-positive integer when $Im (z) = 0.0$ .
2: $k$ – Integer Input: On entry: the function $ψ^{(k)} (z)$ to be evaluated.

Constraint: $0 \leq k \leq 4$ .
3: $ifail$ – Integer Input/Output: On entry: ifail must be set to $0$ , $−1$ or $1$ to set behaviour on detection of an error; these values have no effect when no error is detected.
A value of $0$ causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of $−1$ means that an error message is printed while a value of $1$ means that it is not.

If halting is not appropriate, the value $−1$ or $1$ is recommended. If message printing is undesirable, then the value $1$ is recommended. Otherwise, the value $0$ is recommended. When the value $- 1$ or $1$ is used it is essential to test the value of ifail on exit.

On exit: $ifail = 0$ unless the routine detects an error or a warning has been flagged (see Section 6).

6 Error Indicators and Warnings

If on entry

ifail = 0

−1

, explanatory error messages are output on the current error message unit (as defined by x04aaf).

Errors or warnings detected by the routine:

$ifail = 1$: On entry, $k = ⟨ value ⟩$ .
Constraint: $k \leq 4$ .

On entry, $k = ⟨ value ⟩$ .
Constraint: $k \geq 0$ .

On entry, $Re (z)$ is ‘too close’ to a non-positive integer when $Im (z) = 0.0$ : $Re (z) = ⟨ value ⟩$ , $nint (Re (z)) = ⟨ value ⟩$ .

$ifail = 2$: Evaluation abandoned due to likelihood of overflow.

$ifail = - 99$: An unexpected error has been triggered by this routine. Please contact NAG.
See Section 7 in the Introduction to the NAG Library FL Interface for further information.

$ifail = - 399$: Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library FL Interface for further information.

$ifail = - 999$: Dynamic memory allocation failed.
See Section 9 in the Introduction to the NAG Library FL Interface for further information.

7 Accuracy

Empirical tests have shown that the maximum relative error is a loss of approximately two decimal places of precision.

8 Parallelism and Performance

Background information to multithreading can be found in the Multithreading documentation.

s14aff is not threaded in any implementation.

9 Further Comments

None.

10 Example

This example evaluates the psi (trigamma) function

ψ^{(1)} (z)

z = - 1.5 + 2.5 i

, and prints the results.

s14af: FL CL CPP AD PY MB

NAG FL Interfaces14aff (psi_​deriv_​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 FL Interface
s14aff (psi_deriv_complex)