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Matrix representations for multiplicative nested sums

Volume 158 / 2019

Lin Jiu, Diane Yahui Shi Colloquium Mathematicum 158 (2019), 183-194 MSC: Primary 11M50; Secondary 05A19. DOI: 10.4064/cm7481-10-2018 Published online: 29 July 2019


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.


  • Lin JiuDepartment of Mathematics and Statistics
    Dalhousie University
    6316 Coburg Road
    PO BOX 15000
    Halifax, Nova Scotia
    Canada B3H 4R2
  • Diane Yahui ShiSchool of Mathematics
    Tianjin University
    No. 92 Weijin Road
    Nankai District
    Tianjin, P.R. China 300072

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