Formula:DLMF:25.11:E12

<< Formula:DLMF:25.11:E11

formula in Hurwitz Zeta Function

Formula:DLMF:25.11:E13 >>

${\displaystyle{\displaystyle{\displaystyle\HurwitzZeta@{n+1}{a}=\frac{(-1)^{n+1}{\psi^{(n)}}\left(a\right)}{n!}}}}$

Constraint(s)

${\displaystyle{\displaystyle{\displaystyle n=1,2,3,\dots}}}$ &
${\displaystyle{\displaystyle{\displaystyle\Re{a}>0}}}$

Proof

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Symbols List

& : logical and
${\displaystyle{\displaystyle{\displaystyle\zeta}}}$ : Hurwitz zeta function : http://dlmf.nist.gov/25.11#E1
${\displaystyle{\displaystyle{\displaystyle(-1)}}}$ : negative unity to an integer power : http://dlmf.nist.gov/5.7.E7
${\displaystyle{\displaystyle{\displaystyle\psi}}}$ : psi (or digamma) function : http://dlmf.nist.gov/5.2#E2
${\displaystyle{\displaystyle{\displaystyle\Re{z}}}}$ : real part : http://dlmf.nist.gov/1.9#E2

Bibliography

Equation (12), Section 25.11 of DLMF.

URL links

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<< Formula:DLMF:25.11:E11

formula in Hurwitz Zeta Function

Formula:DLMF:25.11:E13 >>