Difference between revisions of "Hurwitz zeta"
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The Hurwitz zeta function is a generalization of the [[Riemann zeta function]] defined initially for $\mathrm{Re}(s)>1$ and $\mathrm{Re}(a)>0$ by | The Hurwitz zeta function is a generalization of the [[Riemann zeta function]] defined initially for $\mathrm{Re}(s)>1$ and $\mathrm{Re}(a)>0$ by | ||
| − | $$\zeta( | + | $$\zeta(z,q)= \displaystyle\sum_{k=0}^{\infty} \dfrac{1}{(k+q)^z}.$$ |
=Properties= | =Properties= | ||
Revision as of 19:37, 5 September 2016
The Hurwitz zeta function is a generalization of the Riemann zeta function defined initially for $\mathrm{Re}(s)>1$ and $\mathrm{Re}(a)>0$ by $$\zeta(z,q)= \displaystyle\sum_{k=0}^{\infty} \dfrac{1}{(k+q)^z}.$$
Properties
Hurwitz zeta absolute convergence
Relationship between Hurwitz zeta and gamma function
Relation between polygamma and Hurwitz zeta
Bernoulli polynomial and Hurwitz zeta
Catalan's constant using Hurwitz zeta
