arXiv subjects
Publications and source records attributed to Masahiro Igarashi.
We show that a duality formula for certain parametrized multiple series yields numerous relations among them. As a result, we obtain a new relation among extended multiple zeta values, which is an extension of Ohno's relation for multiple zeta values. We do the same study also to multiple Hurwitz zeta values, and obtain a new identity for them.
We prove some generalizations of the sum formula for multiple zeta values by using Hiroyuki Ochiai's method of proving the sum formula.
We prove the cyclic sum formulas for certain two-parameter multiple series. These are new and non-trivial generalizations of the cyclic sum formulas for multiple zeta values and multiple zeta-star values.
I obtain new evaluations of special values of multiple polylogarithms by using a limiting case of a basic hypergeometric identity of G. E. Andrews.
In this note, by using several ideas of other researchers, we derive several relations among multiple zeta-star values from the hypergeometric identities of C. Krattenthaler and T. Rivoal.
In this paper, we prove that certain parametrized multiple series which generalize multiple zeta values satisfy the same relation as Ohno's relation for multiple zeta values. This is a parametrized generalization of Ohno's relation for multiple zeta values. By virtue of this generalization, we obtain a certain equivalence between the relation for the parametrized multiple series and its subfamily. As applications of the above results, we obtain some results for multiple zeta values.