  We device a new method to calculate a large number of Mellin moments of
single scale quantities using the systems of differential and/or difference
equations obtained by integration-by-parts identities between the corresponding
Feynman integrals of loop corrections to physical quantities. These scalar
quantities have a much simpler mathematical structure than the complete
quantity. A sufficiently large set of moments may even allow the analytic
reconstruction of the whole quantity considered, holding in case of first order
factorizing systems. In any case, one may derive highly precise numerical
representations in general using this method, which is otherwise completely
analytic.
