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Lehmer's Interesting Series
- Publication Year :
- 2010
-
Abstract
- The series $$S_k(z)=\sum_{m=1}^{\infty}\frac{m^kz^m}{(\{array}{c} 2m m \{array})}$$ is evaluated in non-recursive closed and analytically continued beyond its domain of convergence $0\le |z|<4$ for $k=0,1,2,\...$. From this we provide a firm basis for Lehmer's observation that $\pi$ emerges from the limiting behavior of $S_k(2)$ as $k\rightarrow\infty$.<br />Comment: 14 pages
- Subjects :
- Mathematical Physics
Mathematics - Number Theory
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1009.4274
- Document Type :
- Working Paper