Single-scale quantities, like the QCD anomalous dimensions and Wilson coefficients, obey difference equations. Therefore their analytic form can be determined from a finite number of moments. We demonstrate this in an explicit calculation by establis
hing and solving large scale recursions by means of computer algebra for the anomalous dimensions and Wilson coefficients in unpolarized deeply inelastic scattering from their Mellin moments to 3-loop order.
We show how Turans inequality $P_n(x)^2-P_{n-1}(x)P_{n+1}(x)geq 0$ for Legendre polynomials and related inequalities can be proven by means of a computer procedure. The use of this procedure simplifies the daily work with inequalities. For instance,
we have found the stronger inequality $|x|P_n(x)^2-P_{n-1}(x)P_{n+1}(x)geq 0$, $-1leq xleq 1$, effortlessly with the aid of our method.
