D. Broadhurst

activity

19922023

most citedThe Multiple Zeta Value Data Mine

343 citations · 1.3k across the 39 of their papers we have counts for

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3 papers · 1 filter

math.CA1999★ 24 cited

Special Values of Multiple Polylogarithms

Jonathan M. Borwein, David M. Bradley, David J. Broadhurst +1

Historically, the polylogarithm has attracted specialists and non-specialists alike with its lovely evaluations. Much the same can be said for Euler sums (or multiple harmonic sums…

math.CA1999★ 18 cited

A seventeenth-order polylogarithm ladder

David H. Bailey, David J. Broadhurst

Cohen, Lewin and Zagier found four ladders that entail the polylogarithms $Li_{n} (α_{1}^{- k}) := \sum_{r > 0} α_{1}^{- k r} / r^{n}$ at order $n = 16$ , with indices $k \leq 360$ , and $α_{1}$ being…

math.CA1998

Polylogarithmic ladders, hypergeometric series and the ten millionth digits of $ζ (3)$ and $ζ (5)$

D. J. Broadhurst

We develop ladders that reduce $ζ (n) := \sum_{k > 0} k^{- n}$ , for $n = 3, 5, 7, 9, 11$ , and $β (n) := \sum_{k \geq 0} (- 1)^{k} (2 k + 1)^{- n}$ , for $n = 2, 4, 6$ , to convergent polylogarithms and products of…

Special Values of Multiple Polylogarithms

A seventeenth-order polylogarithm ladder

Polylogarithmic ladders, hypergeometric series and the ten millionth digits of ζ(3) and ζ(5)

Polylogarithmic ladders, hypergeometric series and the ten millionth digits of $ζ (3)$ and $ζ (5)$