Experimental evaluation of Euler series

Title: Experimental evaluation of Euler series
Creator: Bailey, David H.; Borwein, Jonathan M.; Girgensohn, Roland
Relation: Experimental Mathematics Vol. 3, Issue 1, p. 17-30
Publisher Link: http://dx.doi.org/10.1080/10586458.1994.10504573
Publisher: A K Peters
Resource Type: journal article
Date: 1994
Description: Euler expressed certain sums of the form sum_{k=1}∧infty Bigl(1 + {1 over 2∧m} + cdots + {1 over k∧m}Bigr) (k + 1)∧{-n}hbox{,} where m and n are positive integers, in terms of the Riemann zeta function. In [Borwein et al. 1993], Euler's results were extended to a significantly larger class of sums of this type, including sums with alternating signs. This research was facilitated by numerical computations using an algorithm that can determine, with high confidence, whether or not a particular numerical value can be expressed as a rational linear combination of several given constants. The present paper presents the numerical techniques used in these computations and lists many of the experimental results that have been obtained.
Subject: Euler sums; Riemann zeta function; algorithms; computations
Identifier: http://hdl.handle.net/1959.13/1042521
Identifier: uon:14064
Identifier: ISSN:1058-6458
Language: eng
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