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Full-Text Articles in Physical Sciences and Mathematics
Families Of Weighted Sum Formulas For Multiple Zeta Values, Li Guo, Peng Lei, Jianqiang Zhao
Families Of Weighted Sum Formulas For Multiple Zeta Values, Li Guo, Peng Lei, Jianqiang Zhao
Department of Mathematical Sciences Faculty Publications
Euler's sum formula and its multi-variable and weighted generalizations form a large class of the identities of multiple zeta values. In this paper, we prove a family of identities involving Bernoulli numbers and apply them to obtain infinitely many weighted sum formulas for double zeta values and triple zeta values where the weight coefficients are given by symmetric polynomials. We give a general conjecture in arbitrary depth at the end of the paper.
A Family Of Multiple Harmonic Sum And Multiple Zeta Star Value Identities, Erin Linebarger, Jianqiang Zhao
A Family Of Multiple Harmonic Sum And Multiple Zeta Star Value Identities, Erin Linebarger, Jianqiang Zhao
Department of Mathematical Sciences Faculty Publications
In this paper we present a new family of identities for multiple harmonic sums which generalize a recent result of Hessami Pilehrood et al [Trans. Amer. Math. Soc. (to appear)]. We then apply it to obtain a family of identities relating multiple zeta star values to alternating Euler sums. In such a typical identity the entries of the multiple zeta star values consist of blocks of arbitrarily long 2-strings separated by positive integers greater than two while the largest depth of the alternating Euler sums depends only on the number of 2-string blocks but not on their lengths.