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Conventionally, one calculates a zero in a beta function by computing thisfunction to a given loop order and solving for the zero. Here we discuss adifferent method which is applicable in theories where one can perform apartial diagrammatic summation to infinite-loop order. We show that thismethod, compared with the conventional method, yields much better agreementwith exact results in the case of an asymptotically free gauge theory with${\cal N}=1$ supersymmetry. Applications to other field theories are alsodiscussed.

Analysis of a Zero of a Beta Function Using All-Orders Summation of Diagrams