Programm des Emmy-Noether-Seminars

Fri, 16.11.2018, 14:30

Fri, 16.11.2018, 15:30
Deriving asymptotics for factorially divergent power series

Speaker: Michael Borinsky (Amsterdam)
Host: O. Schnetz
Room: 04.363

If a sequence can be interpreted as the Taylor expansion of an analytic function, it is usually easy to calculate the sequence' asymptotic behaviour by analysing the respective function's singularities. If the coefficients of the sequence grow too fast, we cannot associate a function to the sequence, as the resulting Taylor expansion would have a vanishing radius of convergence. In this case, singularity analysis becomes inapplicable to extract the asymptotics. However, if we restrict ourselves to the subspace of sequences which grow as n!, rich algebraic structures can be found. These structures allow the efficient extraction of asymptotics in a completely algebraic way.