  Two identities extracted from the literature are coupled to obtain an
integral equation for Riemann's $\xi(s)$ function, and thus $\zeta(s)$
indirectly. The equation has a number of simple properties from which useful
derivations flow, the most notable of which relates $\zeta(s)$ anywhere in the
critical strip to its values on a line anywhere else in the complex plane. From
this, I obtain both an analytic expression for $\zeta(\sigma+it)$ everywhere
inside the asymptotic ($t\rightarrow\infty)$ critical strip, and an approximate
solution, within the confines of which the Riemann Hypothesis is shown to be
true. The approximate solution predicts a simple, but strong correlation
between the real and imaginary components of $\zeta(\sigma+it)$ for different
values of $\sigma$ and equal values of $t$; this is illustrated in a number of
Figures.
