Matrix Representation for Multiplicative Nested Sums
Combinatorics
2017-12-27 v3 Number Theory
Probability
Abstract
We study multiplicative nested sums, which are generalizations of harmonic sums, and provide a calculation through multiplication of index matrices. Special cases interpret the index matrices 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 of the index matrices. Combinatorial identities and their generalizations can also be derived from this computation.
Cite
@article{arxiv.1611.02425,
title = {Matrix Representation for Multiplicative Nested Sums},
author = {Lin Jiu and Diane Yahui Shi},
journal= {arXiv preprint arXiv:1611.02425},
year = {2017}
}