Formula:DLMF:25.11:E41

<< Formula:DLMF:25.11:E39

formula in Hurwitz Zeta Function

Formula:DLMF:25.11:E42 >>

${\displaystyle{\displaystyle{\displaystyle\HurwitzZeta@{s}{a+1}=\RiemannZeta@{s}-s\RiemannZeta@{s+1}a+\BigO@{a^{2}}}}}$

Constraint(s)

${\displaystyle{\displaystyle{\displaystyle a\to 0}}}$ with ${\displaystyle{\displaystyle{\displaystyle s}}}$ ${\displaystyle{\displaystyle{\displaystyle(\neq 1)}}}$ fixed

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle\zeta}}}$ : Hurwitz zeta function : http://dlmf.nist.gov/25.11#E1
${\displaystyle{\displaystyle{\displaystyle\zeta}}}$ : Riemann zeta function : http://dlmf.nist.gov/25.2#E1
${\displaystyle{\displaystyle{\displaystyle O}}}$ : order not exceeding : http://dlmf.nist.gov/2.1#E3

Bibliography

Equation (41), Section 25.11 of DLMF.

URL links

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<< Formula:DLMF:25.11:E39

formula in Hurwitz Zeta Function

Formula:DLMF:25.11:E42 >>