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 | ||
$$\zeta(z,q)= \displaystyle\sum_{k=0}^{\infty} \dfrac{1}{(k+q)^z}.$$ | $$\zeta(z,q)= \displaystyle\sum_{k=0}^{\infty} \dfrac{1}{(k+q)^z}.$$ | ||
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[[Bernoulli polynomial and Hurwitz zeta]]<br /> | [[Bernoulli polynomial and Hurwitz zeta]]<br /> | ||
[[Catalan's constant using Hurwitz zeta]]<br /> | [[Catalan's constant using Hurwitz zeta]]<br /> | ||
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| + | =See Also= | ||
| + | [[Riemann zeta]]<br /> | ||
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[[Category:SpecialFunction]] | [[Category:SpecialFunction]] | ||
Revision as of 01:26, 21 December 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
