Prove series form of fractional harmonic numbers – math.stackexchange.com

Prove series form of fractional harmonic numbers – math.stackexchange.com

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Let $H_\alpha$ be the $\alpha$th fractional harmonic number so that $$ H_\alpha = \int_0^1 \frac{1-x^\alpha}{1-x}\,\text dx. $$ I want to directly show $$ H_\alpha = \sum_{k=1}^\infty ...

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