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A new powerful method to calculate Feynman diagrams is proposed. It consistsin setting up a Taylor series expansion in the external momenta squared (ingeneral multivariable). The Taylor coefficients are obtained from the originaldiagram by differentiation and putting the external momenta equal to zero,which means a great simplification. It is demonstrated that it is possible toobtain by analytic continuation of the original series high precision numericalvalues of the Feynman integrals in the whole cut plane. For this purposeconformal mapping and subsequent resummation by means of Pad\'{e} approximantsor Levin transformation are applied.Comment: 21 pages, Bielefeld Unviersity preprint BI-TP %%93-7

Calculation of Feynman diagrams from their small momentum expansion