NAG Toolbox: nag_specfun_psi_deriv_complex (s14af)

Purpose

Syntax

Description

References

Parameters

Compulsory Input Parameters

1:     $\mathrm{z}$ – complex scalar

The argument $z$ of the function.

Constraint: $\mathrm{Re}\left(\mathbf{z}\right)$ must not be ‘too close’ (see Error Indicators and Warnings) to a non-positive integer when $\mathrm{Im}\left(\mathbf{z}\right)=0.0$.

2:     $\mathrm{k}$ – int64int32nag_int scalar

The function ${\psi }^{\left(k\right)}\left(z\right)$ to be evaluated.

Constraint: $0\le \mathbf{k}\le 4$.

Optional Input Parameters

None.

Output Parameters

1:     $\mathrm{result}$ – complex scalar

The result of the function.

2:     $\mathrm{ifail}$ – int64int32nag_int scalar

$\mathbf{ifail}=\mathbf{0}$ unless the function detects an error (see Error Indicators and Warnings).

Error Indicators and Warnings

   $\mathbf{ifail}=1$

On entry,	$\mathbf{k}<0$,
or	$\mathbf{k}>4$,
or	$\mathrm{Re}\left(\mathbf{z}\right)$ is ‘too close’ to a non-positive integer when $\mathrm{Im}\left(\mathbf{z}\right)=0.0$. That is, $\mathrm{abs}\left(\mathrm{Re}\left(\mathbf{z}\right)-\mathrm{nint}\left(\mathrm{Re}\left(\mathbf{z}\right)\right)\right)<\mathit{machine precision}\times \mathrm{nint}\left(\mathrm{abs}\left(\mathrm{Re}\left(\mathbf{z}\right)\right)\right)$.

   $\mathbf{ifail}=2$

The evaluation has been abandoned due to the likelihood of overflow. The result is returned as zero.

   $\mathbf{ifail}=-99$

An unexpected error has been triggered by this routine. Please contact NAG.

   $\mathbf{ifail}=-399$

Your licence key may have expired or may not have been installed correctly.

   $\mathbf{ifail}=-999$

Dynamic memory allocation failed.

Accuracy

Further Comments

Example

Open in the MATLAB editor: s14af_example

function s14af_example


fprintf('s14af example results\n\n');

z =  -1.5 + 2.5i;
k = int64(1);
[pk, ifail] = s14af(z, k);

disp('      z        k      (d^K/dx^K)psi(z)');
fprintf('%5.1f%+5.1fi%5d', real(z), imag(z), k);
fprintf('  %12.4e%+12.4ei\n', real(pk), imag(pk));

s14af example results

      z        k      (d^K/dx^K)psi(z)
 -1.5 +2.5i    1   -1.9737e-01 -2.4271e-01i