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If a series representation of ${\gamma}$ The Euler-Mascheroni constant is:$\displaystyle\sum_{k=1}^{+\infty}\left[\frac 1 k -\log\left(1+\frac 1 k\right)\right]$ then what is the series representation of $\displaystyle\frac{1}{\gamma}$ ?.

robjohn
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    "The series representation" should really be "A series representation" since there's a lot of them – Yuriy S Feb 16 '18 at 21:13
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    It is rarely simple to derive a series representation for $\frac{1}{\alpha}$, given a series representation for $\alpha$. And $\gamma$ is the Euler-Mascheroni constant. – Jack D'Aurizio Feb 16 '18 at 21:20
  • There's a regular generalized continued fraction representation of $\gamma$, which trivially is also a representation of $1/ \gamma$, since it's a fraction. The details and the reference to the paper where it was given, are in this answer – Yuriy S Feb 16 '18 at 21:33
  • A very serious joke: $1/\gamma + 0 + 0 + 0 + \cdots$ – Martín-Blas Pérez Pinilla Feb 17 '18 at 11:33

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