  This pre-print deals with the one dimensional Hubbard model, as described by
the Pseudofermion Dynamical Theory (PDT), with the purpose of (1) deriving a
novel expression for the one electron spectral function for all values of the
on-site repulsion $U/t$ and filling $n \in (0,1)$, at vanishing magnetisation
$m \rightarrow 0$, and (2) discover how to correctly compare the results
originating from two different theoretical frameworks in the $U/t \rightarrow
\infty$ limit, as a first-test of the novel expressions obtained in this paper.
Thus, an exact expression of the spectral function is obtained, which is
furthermore successfully compared with previously known results in the $U
\rightarrow \infty$ limit.
  Following the PDT, the expression for the one electron spectral function
factorises into a spin part and a charge part for all values of the on-site
repulsion $U/t$, where the dynamical quantum objects are spin zero and
$\eta$-spin (charge) zero singlet pairs of so-called rotated electrons, which
in turn are obtained from the original electrons by a unitary transformation.
The spectral function is exemplified for $U/t = 400$, with the purpose of
comparing it with the same function obtained by other authors (and other means)
in the $U \rightarrow \infty$ limit.
  The main pillars of the PDT is presented in a summarised form. For example,
we will only be interested in excited energy eigenstates which originate the
most significant singular features of the spectral map in the $(k,\omega)$
plane, safely ignoring higher order contributions. Even though emphasis is
given on step-by-step derivations where necessary, derivations that have been
done elsewhere and/or do not notably contribute to the physical understanding,
are sometimes avoided. Therefore, references for further study are given
throughout the paper.
