Evaluation of simple Feynman graphs

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Abstract
A number of one‐loop graphs with arbitrary external momenta and internal masses contributing to the perturbation expansion of a Euclidean φ4 theory are evaluated exactly in three and two dimensions. The final expressions are simple closed forms involving elementary functions only. A method for handling the multidimensional angular integrations that arise in calculations of massless QED or φ4 in four dimensions is also discussed.