Generalized Harmonic, Cyclotomic, and Binomial Sums, their Polylogarithms and Special Numbers
Abstract
A survey is given on mathematical structures which emerge in multiloop Feynman diagrams. These are multiply nested sums, and, associated to them by an inverse Mellin transform, specific iterated integrals. Both classes lead to sets of special numbers. Starting with harmonic sums and polylogarithms we discuss recent extensions of these quantities as cyclotomic, generalized (cyclotomic), and binomially weighted sums, associated iterated integrals and special constants and their relations.
 Publication:

Journal of Physics Conference Series
 Pub Date:
 June 2014
 DOI:
 10.1088/17426596/523/1/012060
 arXiv:
 arXiv:1310.5645
 Bibcode:
 2014JPhCS.523a2060A
 Keywords:

 Mathematical Physics;
 High Energy Physics  Phenomenology;
 High Energy Physics  Theory
 EPrint:
 10 pages, Proceedings ACAT 2013