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Lehmer's Interesting Series
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 for . From this we
provide a firm basis for Lehmer's observation that emerges from the
limiting behavior of as .Comment: 14 page