  The Gauge Technique has been applied to QED$_{2+1}$ in the quenched case with
infrared subtraction. The behaviour of the fermion propagator near the
threshold is then found to be \[ S(p)\to \frac{(\gamma \cdot
p+m)}{(p^{2}-m^{2})}(\frac{p^{2}-m^{2}}{% 2m^{2}})^{\zeta}\exp (-\frac{\eta
\varsigma}{2}), \] where $\varsigma =e^{2}/(4\pi m)$ and this is gauge
invariant except the exponential factor. We also find a spectral function in
the Landau and Yennie like gauge. The propagators $S(p)$ are expressed in terms
of $\Phi (z,1,\varsigma)$ explicitly .The vacuum expectation value $<
\overline{\psi}\psi >$ is gauge dependent . Thus dynamical mass generation does
not occur.
