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To complete the reduction to standard form (the first step), note that the combined denominator D always has the form

where k is the internal loop momentum and Q is a vector function of the external r omenta and the Feynman parameters. Thus the square of the denominator can always be completed by shifting k = k' — Q, which gives

This shift must also be carried out in the numerator N, which assumes the general form

where the Ni are tensors which do not depend on k'. Since the denominator is even in k' (in fact, it depends on k'2 only), all of the odd terms reduce to zero and the even ones can be simplified using the following identities:

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