Formula:DLMF:25.16:E12

<< Formula:DLMF:25.16:E11

formula in Mathematical Applications

Formula:DLMF:25.16:E13 >>

${\displaystyle{\displaystyle{\displaystyle\GenEulerSumH@{s}{z}+\GenEulerSumH@{z}{s}=\RiemannZeta@{s}\RiemannZeta@{z}+\RiemannZeta@{s+z}}}}$

Constraint(s)

both ${\displaystyle{\displaystyle{\displaystyle\GenEulerSumH@{s}{z}}}}$ and ${\displaystyle{\displaystyle{\displaystyle\GenEulerSumH@{z}{s}}}}$ are finite

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle H}}}$ : generalized Euler sums : http://dlmf.nist.gov/25.16#SS2.p7
${\displaystyle{\displaystyle{\displaystyle\zeta}}}$ : Riemann zeta function : http://dlmf.nist.gov/25.2#E1

Bibliography

Equation (12), Section 25.16 of DLMF.

URL links

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