Abstract
Abstract The high-temperature expansion of many field theoretic quantities leads to double (or triple) infinite series. These series are completely convergent (i.e. finite). In order to collect together common powers of temperature one would like to interchange the order of thessummations, but such an interchange produces a divergent series (formally a zeta function for a negative argument). This paper proves some theorems that allow one to express the (finite) result as a power series in temperature.
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