Clemens G. Raab

Iterated binomial sums and their associated iterated integrals

We consider finite iterated generalized harmonic sums weighted by the binomial

Calculating massive 3-loop graphs for operator matrix elements by the method of hyperlogarithms

\binom{2k}{k}

Iterated Elliptic and Hypergeometric Integrals for Feynman Diagrams

in numerators and denominators. A large class of these functions emerges in the calculation of massive Feynman diagrams with local operator insertions starting at 3-loop order in the coupling constant and extends the classes of the nested harmonic, generalized harmonic and cyclotomic sums. The binomially weighted sums are associated by the Mellin transform to iterated integrals over square-root valued alphabets. The values of the sums for

New Results on the 3-Loop Heavy Flavor Wilson Coefficients in Deep-Inelastic Scattering

N \rightarrow \infty

Non-planar Feynman integrals, Mellin-Barnes representations, multiple sums

and the iterated integrals at

Three-Loop Contributions to the Gluonic Massive Operator Matrix Elements at General Values of N

x=1

Nested (inverse) binomial sums and new iterated integrals for massive Feynman diagrams

lead to new constants, extending the set of special numbers given by the multiple zeta values, the cyclotomic zeta values and special constants which emerge in the limit

Solving linear ordinary differential systems in hyperexponential extensions

N \rightarrow \infty

Integration of unspecified functions and families of iterated integrals

of generalized harmonic sums. We develop algorithms to obtain the Mellin representations of these sums in a systematic way. They are of importance for the derivation of the asymptotic expansion of these sums and their analytic continuation to

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

N \in \mathbb{C}