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Various of the single scale quantities in massless and massive QCD up to3-loop order can be expressed by iterative integrals over certain classes ofalphabets, from the harmonic polylogarithms to root-valued alphabets. Examplesare the anomalous dimensions to 3-loop order, the massless Wilson coefficientsand also different massive operator matrix elements. Starting at 3-loop order,however, also other letters appear in the case of massive operator matrixelements, the so called iterative non-iterative integrals, which are related tosolutions based on complete elliptic integrals or any other special functionwith an integral representation that is definite but not a Volterra-typeintegral. After outlining the formalism leading to iterative non-iterativeintegrals,we present examples for both of these cases with the 3-loop anomalousdimension $\gamma_{qg}^{(2)}$ and the structure of the principle solution inthe iterative non-interative case of the 3-loop QCD corrections to the$\rho$-parameter.

Iterative and Iterative-Noniterative Integral Solutions in 3-Loop Massive QCD Calculations