Formula:DLMF:25.11:E42

<< Formula:DLMF:25.11:E41

formula in Hurwitz Zeta Function

Formula:DLMF:25.11:E43 >>

${\displaystyle{\displaystyle{\displaystyle\HurwitzZeta@{s}{\alpha+\mathrm{i}\beta}\to 0}}}$

Constraint(s)

${\displaystyle{\displaystyle{\displaystyle\beta\to\pm\infty}}}$ with ${\displaystyle{\displaystyle{\displaystyle s}}}$ fixed &
${\displaystyle{\displaystyle{\displaystyle\Re s>1}}}$

Note(s)

uniformly with respect to bounded nonnegative values of ${\displaystyle{\displaystyle{\displaystyle\alpha}}}$

Proof

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Symbols List

& : logical and
${\displaystyle{\displaystyle{\displaystyle\zeta}}}$ : Hurwitz zeta function : http://dlmf.nist.gov/25.11#E1
${\displaystyle{\displaystyle{\displaystyle\mathrm{i}}}}$ : imaginary unit : http://dlmf.nist.gov/1.9.i
${\displaystyle{\displaystyle{\displaystyle\Re{z}}}}$ : real part : http://dlmf.nist.gov/1.9#E2

Bibliography

Equation (42), Section 25.11 of DLMF.

URL links

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<< Formula:DLMF:25.11:E41

formula in Hurwitz Zeta Function

Formula:DLMF:25.11:E43 >>