Formula:DLMF:25.2:E4

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formula in Definition and Expansions

Formula:DLMF:25.2:E6 >>

${\displaystyle{\displaystyle{\displaystyle\RiemannZeta@{s}=\frac{1}{s-1}+\sum_{n=0}^{\infty}\frac{(-1)^{n}}{n!}\gamma_{n}(s-1)^{n}}}}$

Constraint(s)

${\displaystyle{\displaystyle{\displaystyle\Re{s}>0}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle\zeta}}}$ : Riemann zeta function : http://dlmf.nist.gov/25.2#E1
${\displaystyle{\displaystyle{\displaystyle\Sigma}}}$ : sum : http://drmf.wmflabs.org/wiki/Definition:sum
${\displaystyle{\displaystyle{\displaystyle(-1)}}}$ : negative unity to an integer power : http://dlmf.nist.gov/5.7.E7
${\displaystyle{\displaystyle{\displaystyle\gamma_{n}}}}$ : Stieltjes constants : http://drmf.wmflabs.org/wiki/Definition:StieltjesConstants
${\displaystyle{\displaystyle{\displaystyle\Re{z}}}}$ : real part : http://dlmf.nist.gov/1.9#E2

Bibliography

Equation (4), Section 25.2 of DLMF.

URL links

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