Generalized Harmonic, Cyclotomic, and Binomial Sums, their Polylogarithms and Special Numbers

15th International Workshop on Advanced Computing and Analysis Techniques in Physics Research

物理学;计算机科学

Ablinger, J.^1 ; Blümlein, J.^2 ; Schneider, C.^1

Research Institute for Symbolic Computation (RISC), Johannes Kepler University, Altenbergerstraße 69, A-4040 Linz, Austria^1

Deutsches Elektronen-Synchrotron, DESY, Platanenallee 6, D-15738 Zeuthen, Germany^2

关键词: Feynman diagrams;    Inverse Mellin transforms;    Iterated integrals;    Mathematical structure;    Multi-loops;    Polylogarithms;    Weighted Sum;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/523/1/012060/pdf
DOI  :  10.1088/1742-6596/523/1/012060

学科分类：计算机科学（综合）

来源: IOP

【 摘 要 】

A survey is given on mathematical structures which emerge in multi-loop 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.