A generalization of multiple zeta values. Part 2: Multiple sums

Sums of the form $\sum_{q \leq N_1 < \cdots N_m n}{a_{(m);N_m}\cdots a_{(2);N_2}a_{(1);N_1}}$ date back to sixteen century when Vi\`ete illustrated that relation linking roots and coefficients a polynomial had this form. In more recent years, such sums have become increasingly used with diversity applications. paper, we develop formulae help manipulating (which will refer as multiple sums). We variation express in terms lower order sums. Additionally, derive set partition identities use prove reduction theorem expresses combination simple (non-recurrent) present variety applications including concerning polynomials MZVs well generalization binomial theorem. Finally, establish connection between type called recurrent By exploiting connection, provide additional for odd even partitions.