Formula:DLMF:25.11:E11

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Failed to parse (unknown function "\HurwitzZeta"): {\displaystyle {\displaystyle \HurwitzZeta@{s}{\tfrac{1}{2}} = (2^s - 1) \RiemannZeta@{s} }}

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Proof

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Failed to parse (unknown function "\RiemannZeta"): {\displaystyle {\displaystyle \RiemannZeta@{s} = \frac{1}{1 - 2^{-s}} \sum_{n=0}^\infty \frac{1}{(2n+1)^s} }}
and
Failed to parse (unknown function "\HurwitzZeta"): {\displaystyle {\displaystyle \HurwitzZeta@{s}{a} = \sum_{n=0}^\infty \frac{1}{(n+a)^s} }} .


Symbols List

 : Hurwitz zeta function : http://dlmf.nist.gov/25.11#E1
 : Riemann zeta function : http://dlmf.nist.gov/25.2#E1

Bibliography

Equation (11), Section 25.11 of DLMF.

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