# Formula:DLMF:25.11:E44

${\displaystyle{\displaystyle{\displaystyle\HurwitzZeta^{\prime}@{-1}{a}-\frac{% 1}{12}+\frac{1}{4}a^{2}-\left(\frac{1}{12}-\frac{1}{2}a+\frac{1}{2}a^{2}\right% )\ln a\sim-\sum_{k=1}^{\infty}\frac{\BernoulliB{2k+2}}{(2k+2)(2k+1)2k}a^{-2k}}}}$

## Note(s)

primes on ${\displaystyle{\displaystyle{\displaystyle\zeta}}}$ denote derivatives with respect to ${\displaystyle{\displaystyle{\displaystyle s}}}$

## Proof

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