Lehmer's Interesting Series

被引：4

作者：

Dyson, Freeman J. ^{[1
]}

Frankel, Norman E. ^{[2
,3
]}

Glasser, M. Lawrence ^{[4
]}

机构：

[1] Inst Adv Study, Princeton, NJ 08540 USA

[2] Univ Melbourne, Dept Phys, Melbourne, Vic 3010, Australia

[3] Univ Melbourne, Fac Phys, Melbourne, Vic 3010, Australia

[4] Clarkson Univ, Dept Phys, Potsdam, NY USA

来源：

AMERICAN MATHEMATICAL MONTHLY | 2013年 / 120卷 / 02期

关键词：

D O I：

10.4169/amer.math.monthly.120.02.116

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The series S-k(z) =Sigma(infinity)(n=1) [C-m(2m)](-1)m(k)z(m) is evaluated in a nonrecursive and closed process. It can be analytically continued beyond its domain of convergence vertical bar z vertical bar < 4 when k = 0, 1, 2, .... From this we provide a firm basis for Lehmer's observation that g emerges from the limiting behavior of S-k(2) as k -> infinity.

引用

页码：116 / 130

页数：15

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