meromorphic function

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21: Errata

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The original constraint, $\mathrm{\Re }s>0$, was removed because, as stated after (25.2.1), $\zeta \left(s\right)$ is meromorphic with a simple pole at $s=1$, and therefore $\zeta \left(s\right)-{(s-1)}^{-1}$ is an entire function.

Suggested by John Harper.

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22: 25.16 Mathematical Applications

§25.16 Mathematical Applications

… ►which is related to the Riemann zeta function by … ►

§25.16(ii) Euler Sums

… ► $H\left(s\right)$ is analytic for $\mathrm{\Re }s>1$, and can be extended meromorphically into the half-plane $\mathrm{\Re }s>-2k$ for every positive integer $k$ by use of the relations … ►which satisfies the reciprocity law …