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I am using the below function to compute the Hurwitz zeta function from Riemann zeta function. But I am not getting the correct results when compared with the value of Wolfram alpha Hurwitz zeta function. I am suspecting some issues with floating point errors but not sure. Can someone help me out with the explanation ?

function h=hzeta(s,q) z = zeta(s) h = z - sum((1:(q-1)).^(-s));

where q=1-500 and s=1-7

Thanks,

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    Your results are wrong because you misinterpret the Hurwitz zeta function. It's definition is as follows: $$\zeta(s,\nu)=\sum_{n=0}^\infty\frac1{(n+\nu)^s}$$ From here, one can derive the following: $$\zeta(s,\nu)=\zeta(s)+\sum_{n=0}^\infty\frac1{(n+\nu)^s}-\frac1{n^s}$$ which converges for $\Re(s)>0$ and $-\nu\notin\mathbb N$.2017-05-27

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