  We consider the two-loop self-mass sunrise amplitude with two equal masses
$M$ and the external invariant equal to the square of the third mass $m$ in the
usual $d$-continuous dimensional regularization. We write a second order
differential equation for the amplitude in $x=m/M$ and show as solve it in
close analytic form. As a result, all the coefficients of the Laurent expansion
in $(d-4)$ of the amplitude are expressed in terms of harmonic polylogarithms
of argument $x$ and increasing weight. As a by product, we give the explicit
analytic expressions of the value of the amplitude at $x=1$, corresponding to
the on-mass-shell sunrise amplitude in the equal mass case, up to the $(d-4)^5$
term included.
