Limit to 1 of Zeta of s minus Reciprocal of s-1

Theorem

$\ds \lim_{s \mathop \to 1} \paren {\map \zeta s - \dfrac 1 {s - 1} } = \gamma$

where:

$\zeta$ denotes the Riemann $\zeta$ (zeta) function

$\gamma$ denotes the Euler-Mascheroni constant.

Proof

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Sources

• 1983: François Le Lionnais and Jean Brette: Les Nombres Remarquables ... (previous) ... (next): $0,57721 56649 \ldots$