Resolution of Some Open Problems Concerning Multiple Zeta Evaluations of Arbitrary Depth |
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| Authors: | Douglas Bowman David M Bradley |
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| Institution: | (1) Department of Mathematics, Department of Mathematical Sciences, Northern Illinois University, Dekalb, IL, 60115, U.S.A.;(2) Department of Mathematics and Statistics, University of Maine, 5752 Neville Hall, Orono, ME, 04469-5752, U.S.A. |
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| Abstract: | We prove some new evaluations for multiple polylogarithms of arbitrary depth. The simplest of our results is a multiple zeta evaluation one order of complexity beyond the well-known Broadhurst–Zagier formula. Other results we provide settle three of the remaining outstanding conjectures of Borwein, Bradley, and Broadhurst. A complete treatment of a certain arbitrary depth class of periodic alternating unit Euler sums is also given. |
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| Keywords: | multiple zeta values MZV multiple polylogarithms Euler sums hypergeometric functions |
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