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What is the riemann zeta function in the critical strip i.e in Real(s) in [0,1]. I know the formula of riemann function when Re(s)>1 i.e f(s)= 1 + 1/2^s + 1/3^s ... But this doesnt converge for Re(s)<1.So I want to know which formula of riemann zeta is used for Real(s) in [0,1].

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Do you mean you want a formula which explains its values in that strip? Or do you want comments about how it behaves (there's a famous conjecture about that)? – James Cranch Mar 6 2012 at 10:48
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 You have to put a lot more effort into writing a question on this site. – Gerry Myerson Mar 6 2012 at 11:07
I want a formula or series which explains its values in that strip. – Samleo Mar 6 2012 at 12:58
I claim this has been edited so that it now <i>definitely is</i> a real question. – James Cranch Mar 6 2012 at 13:43
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 First read at least the Wikipedia side before asking. There are formulas, e.g. for $s \neq 1$ we have $$\zeta(s) = \frac{2^{s-1}}{s-1}-2^s\!\int_0^{\infty}\!\!\!\frac{\sin(s\arctan t)}{(1+t^2)^\frac{s}{2}(\mathrm{e}^{\pi\,t}+1)}\,\mathrm{d}t$$ – Marc Palm Mar 6 2012 at 14:23
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closed as not a real question by George Lowther, Chandan Singh Dalawat, Marc Palm, Gerry Myerson, Felipe Voloch Mar 6 2012 at 13:19

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