  In this paper we present a simple method for deriving an alternative form of
the functional equation for Riemann's Zeta function. The connections between
some functional equations obtained implicitly by Leonhard Euler in his work
"Remarques sur un beau rapport entre les series des puissances tant directes
que reciproques" in Memoires de l'Academie des Sciences de Berlin 17, (1768),
permit to define a special function, named A(s), which is fully symmetric and
is similar to Riemann's "XI" function. To be complete we find several integral
representations of the A(s) function and as a direct consequence of the second
integral representation we obtain also an analytic continuation of the same
function using an identity of Ramanujan.
