psi(z) for Im(z) >> 1?

[Matias Atria <atria@math.upenn.edu>]

Hi,

My apologies if this is already known. There's a problem with the
computation of psi(z) when Im(z) is moderately large. The version of GP I'm
using is

                  GP/PARI CALCULATOR Version 2.1.0 (released)
                i686 running linux (ix86 kernel) 32-bit version
                (readline v2.2 enabled, extended help available)

and I'm getting this:

? psi(1.2+100*I)
%1 = 4.605189310446618887011272357 + 1.563800184428028749658853710*I
? psi(1.2+100.*I)
%2 = 4.605188901735109764779067052 + 1.563794008870291303171926465*I
? \p200
   realprecision = 202 significant digits (200 digits displayed)
? psi(1.2+100.*I)
%3 = 4.6051905(...) + 1.563796(...)*I \\ <-- CORRECT
? \p28
   realprecision = 28 significant digits
? psi(1.2+200*I)
%5 = 3.591026996537060725697785476 + 5.378904945490827754765786142*I
? psi(1.2+200.*I)
%6 = 0.6084323283704262549545579944 + 1.796033268559931806612149379*I
? 
Good bye!

Thanks,
Matias.