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G. Kawashima, “A Generalization of the Duality for Multiple Harmonic Sums,” Journal of Number Theory, Vol. 130, No. 2, 2010, pp. 347-359. doi:10.1016/j.jnt.2009.03.002

has been cited by the following article:

• TITLE: One Step Forward, Two Steps Back: Biconvergence of Washed Harmonic Series

  AUTHORS: Christopher M. Davis, David G. Taylor

  KEYWORDS: Harmonic Series; Biconvergence; Non-Integer Series

  JOURNAL NAME: Advances in Pure Mathematics, Vol.3 No.3, May 8, 2013

  ABSTRACT: We examine variations of the harmonic series by grouping terms into “washings” that alternate sign with the number of terms in a washing growing exponentially with respect to a fixed base. The bases x = 1 and x = ∞ correspond to the alternating harmonic series and the usual harmonic series; we first consider other positive integral bases and further we consider positive real number bases with a unique way to make sense of adding a non-integral number of terms together. In both cases, we prove a remarkable result regarding the difference between the upper and lower convergent values of the series, and give some analysis of this behavior.