Clemens G. Raab

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We propose a general algorithmic approach to noncommutative operator algebras generated by linear operators. Ore algebras are a well-established tool covering many cases arising in applications. However, integro-differential operators, for example, do not fit this structure. Instead of using (parametrized) Gröbner bases in noncommutative polynomial(More)
Let <i>F</i> be a differential field generated from the rational functions over some constant field by one hyperexponential extension. We present an algorithm to compute the solutions in <i>F</i><sup><i>n</i></sup> of systems of <i>n</i> first-order linear ODEs. Solutions in <i>F</i> of a scalar ODE of higher order can be determined by an algorithm of(More)
Hiking is one of the most popular activities among the elderly in Alpine regions. Due to the long-lasting, moderately intensive nature of this form of physical activity, hiking is generally considered to be beneficial to health. However, it is currently unclear whether once-weekly hiking—as commonly practiced at weekends—really does yield such positive(More)
Nested sums containing binomial coefficients occur in the computation of massive operator matrix elements. Their associated iterated integrals lead to alphabets including radicals, for which we determined a suitable basis. We discuss algorithms for converting between sum and integral representations, mainly relying on the Mellin transform. To aid the(More)
Parameter integrals naturally arise as integral transforms or related convolution integrals, for instance. We consider the special case where such integrals originate from expressions involving nested integrals. More precisely, we deal with integrals where the integrand is given by a nested integral multiplied by a parameter-dependent factor. The aim is to(More)
Integrals are important to many applications ranging from physics over engineering to statistics. While systematic methods for symbolic computation of integrals have a long history, computer algebra tools for computation of parameter integrals are a more recent topic. For computing (definite) parameter integrals, one does not necessarily need to know an(More)
We calculate 3-loop master integrals for heavy quark correlators and the 3-loop QCD corrections to the ρ-parameter. They obey non-factorizing differential equations of second order with more than three singularities, which cannot be factorized in Mellin-N space either. The solution of the homogeneous equations is possible in terms of convergent close(More)