  In our previous paper \cite{PTA1} we derived a generic expression for the
pulse redshift the main observable for the Pulsar Timing Array (PTA) experiment
for detection of gravitational waves for all possible polarizations induced by
modifications of general relativity (GR). In this work we provide a generic
expression of the overlap reduction function for PTA without using the short
wavelength approximation for tensorial polarization. We are convinced, that the
short wavelength approximation is not applicable to the overlap reduction
function for PTA's, since the removal of the exponential terms in the integrand
would lead to poles for $x, y$ and $l$ polarizations and discontinuities for
$+$ and $\times$. In this work we provide a series expansion to calculate the
integral exactly and investigate the behaviour of the series for short
wavelength values via numerical evaluation of the analytical series. We find a
disagreement for the limit of co-located pulsars with the Hellings \& Downs
curve.
