  We compute the second moment of the Riemann zeta function for shifted
arguments over a domain that extends the ones in the literature. We use the
Riemann-Siegel formula for the error term in the approximate functional
equation and take the products of all the terms into account. We also show
that, as a function of imaginary shifts on the critical line, the the second
moment behaves like a Fourier-Cauchy type kernel on a class of functions. This
is reminiscent of orthogonal functions.
