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In all mass cases needed for quark and gluon self-energies, the two-loopmaster diagram is expanded at large and small $q^2$, in $d$ dimensions, usingidentities derived from integration by parts. Expansions are given, in terms ofhypergeometric series, for all gluon diagrams and for all but one of the quarkdiagrams; expansions of the latter are obtained from differential equations.Pad\'{e} approximants to truncations of the expansions are shown to be of greatutility. As an application, we obtain the two-loop photon self-energy, for all$d$, and achieve highly accelerated convergence of its expansions in powers of$q^2/m^2$ or $m^2/q^2$, for $d=4$.Comment: 25 pages, OUT--4102--43, BI--TP/92--5

Two-loop two-point functions with masses: asymptotic expansions and Taylor series, in any dimension