The Arithmetic - Harmonic Mean

نویسندگان

  • G. M. Phillips
  • E. T. Copson
  • G. M. PHILLIPS
چکیده

Consider two sequences generated by ",,+ i Mi"„<hn)hn*\ M'i"„+X,b„), where the a„ and b„ are positive and M and M' are means. The paper discusses the nine processes which arise by restricting the choice of M and M' to the arithmetic, geometric and harmonic means, one case being that used by Archimedes to estimate it. Most of the paper is devoted to the arithmetic-harmonic mean, whose limit is expressed as an infinite product and as an infinite series in two ways.

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تاریخ انتشار 2010