nag_complex_polygamma (s14afc) evaluates an approximation to the 
th derivative of the psi function 
given by
![((D@@k)(psi))(z) = d^k*psi(z)/(d*z^k) and d^k*psi(z)/(d*z^k) = d^k*(d*(1/(d*z)), log[e]*GAMMA, z)/(d*z^k)](/support/helpjp/helpview.aspx?si=9761/file08639/math85.png)
where 
is complex provided 
and 
. If 
, 
is real and thus 
is singular when 
.
Note that 
is also known as the polygamma function. Specifically, 
is often referred to as the digamma function and 
as the trigamma function in the literature. Further details can be found in Abramowitz and Stegun (1972).
nag_complex_polygamma (s14afc) is based on a modification of the method proposed by Kölbig (1972).
To obtain the value of 
when 
is real, s14aec (nag_real_polygamma) can be used.
