Matrix representations for multiplicative nested sums
Volume 158 / 2019
Colloquium Mathematicum 158 (2019), 183-194
MSC: Primary 11M50; Secondary 05A19.
DOI: 10.4064/cm7481-10-2018
Published online: 29 July 2019
Abstract
We study multiplicative nested sums, generalizations of harmonic sums, and provide a calculation through multiplication of index matrices. In special cases, the index matrices are interpreted as stochastic transition matrices of random walks on a finite number of sites. Relations among multiplicative nested sums, which are generalizations of relations between harmonic series and multiple zeta functions, can be easily derived from identities for index matrices. Combinatorial identities and their generalizations can also be derived from this computation.
