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Note sur la sommation d’une serie. (French) JFM 46.0343.02

Nouv. Ann. (4) 16, 203-209 (1916).
Man hat \[ \sum_{k=0}^\infty (-1)^k\frac{1}{a+kh}=(-1)^{[\frac {a}{h}]}\frac{\pi}{2h\sin\frac{b\pi}{h}} -\frac{2(-1)^{[\frac{a}{h}]}}{h} \sum_{k=1}^{[\frac {h}{2}]}\cos(2k-1)\frac{b\pi}{h}\cdot\log\sin\frac{2k- 1}{2h} \pi+\sum_{k=1}^{[\frac{a}{h}]}(-1)^{k-1}\frac{1}{a-kh},s \] wobei \(a=b+nh\;(b<h)\) ist.
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