Is there a nice identity known for $$\frac{\zeta(k- \tfrac{1}{2}) \zeta(2k -1)}{\zeta(4k -2)}?$$ (I'm dealing with half-integral $k$.) Equally, an identity for $$\frac{\zeta(s) \zeta(2s)}{\zeta(4s)}$$ would do ;)
Identity for $\zeta(k- 1/2) \zeta(2k -1) / \zeta(4k -2)$?
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riemann-zeta
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0What kind of identity? – 2012-11-28
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0I don't have anything specific in mind, something that makes it nicer (and doesn't bloat it up) ;) It doesn't serve a particular purpose, I was just wondering if there is any... – 2012-11-28
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1If there were a simplification not involving odd $s$ one could evaluate for example zeta(3), which is not now known in closed form. – 2012-11-28