Speaker
Description
We present tools from symbolic summation and integration that are tailored for Feynman integrals.
In particular, we will present algorithms that enable one to produce linear differential or
difference equations that contain the input expression (e.g., in form of definite hypergeometric multisums, hyperexpontial multiintegrals or coupled systems of linear
differential equations) as solution. In a nutshell, we show constructively that
the given input expressions of Feynman integrals are holonomic. Given such equations one can then look for closed form solutions, e.g., in terms of iterative integrals and sums (which are again holonomic). This leads usually to rather compact expressions that can be used for asymptotic expansions or analytic continuation.
We will report on these different tools that we have applied within our long-term cooperation between RISC and DESY (Deutsches Elektronen-Synchrotron)
and demonstrate their flexibility.
