Nested sums, expansion of transcendental functions and multiscale multiloop integrals
By Sven-Olaf Moch, Peter Uwer, Stefan Weinzierl. 2001
337 citations recorded by the source corpus.
Expansion of higher transcendental functions in a small parameter are needed in many areas of science. For certain classes of functions this can be achieved by algebraic means. These algebraic tools are based on nested sums and can be formulated as algorithms suitable for an implementation on a computer. Examples such as expansions of generalized hypergeometric functions or Appell functions are discussed. As a further application, we give the general solution of a two-loop integral, the so-called C-topology, in terms of multiple nested sums. In addition, we discuss some important properties of nested sums, in particular we show that they satisfy a Hopf algebra.
Subfields: Applied Mathematics, Computational Theory and Mathematics
View Paper: https://www.semanticscholar.org/paper/361ef372e7cecde8125f43e0c506afeecb4dbc3c
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
- Falko Dulat
- Claude Duhr
- Bernhard Mistlberger
- Erik Panzer
- C. Anastasiou
- V. Duca
- David John Broadhurst
- Jos Vermaseren
In Computational Theory and Mathematics
- C. Anastasiou
- Jos Vermaseren
- J. Blumlein
- Claude Duhr
- Erik Panzer
- Falko Dulat
- Vladimir A. Smirnov
- Bernhard Mistlberger
Citations in the corpus
- An analytic result for the two-loop hexagon Wilson loop in N = 4 SYM (2010, background): “The infinite sums which appear in the intermediate steps of the computation are typically generalised harmonic sums [43, 44] as well as multiple binomial sums [45, 46].”
- The Multiple Zeta Value data mine (2009, background): “The fact tha hey are depth mixing makes them useless for calculations in which the concept of depth plays a role.”
- Feynman integrals and hyperlogarithms (2015, methodology): “,zr ∈ C we have an associated Z-sum [131] given as6 Z (n;n1, . . . , nr; z1, . . . , zr) := ∑ 0<k1<···<kr≤n zk11 · · · zkrr kn11 · · · k nr r .”