MULTIPLE ZETA VALUES AND ITERATED LOG-SINE INTEGRALS
- 1 January 2020
- journal article
- research article
- Published by Faculty of Mathematics, Kyushu University in Kyushu Journal of Mathematics
- Vol. 74 (2), 233-254
- https://doi.org/10.2206/kyushujm.74.233
Abstract
We introduce an iterated integral version of (generalized) log-sine integrals (iterated log-sine integrals) and prove a relation between a multiple polylogarithm and iterated log-sine integrals. We also give a new method for obtaining relations among multiple zeta values, which uses iterated log-sine integrals, and give alternative proofs of several known results related to multiple zeta values and log-sine integrals.Keywords
This publication has 9 references indexed in Scilit:
- Special values of generalized log-sine integralsPublished by Association for Computing Machinery (ACM) ,2011
- Generalized log sine integrals and the Mordell-Tornheim zeta valuesTransactions of the American Mathematical Society, 2010
- Log-Sine integrals involving series associated with the zeta function and polylogarithmsMATHEMATICA SCANDINAVICA, 2009
- About higher order ɛ-expansion of some massive two- and three-loop master-integralsNuclear Physics B, 2005
- Groupes fondamentaux motiviques de Tate mixteAnnales Scientifiques de lʼÉcole Normale Supérieure, 2005
- Mixed Tate motives and multiple zeta valuesInventiones Mathematicae, 2002
- Central Binomial Sums, Multiple Clausen Values, and Zeta ValuesExperimental Mathematics, 2001
- Values of the Riemann zeta function and integrals involving log(2 sinh(theta/2) and log(2 sin(theta/2)Pacific Journal of Mathematics, 1995
- Values of Zeta Functions and Their ApplicationsPublished by Springer Science and Business Media LLC ,1994