Difference between revisions of "Hurwitz zeta"
From specialfunctionswiki
(→Properties) |
|||
| (8 intermediate revisions by the same user not shown) | |||
| Line 1: | Line 1: | ||
| − | The Hurwitz zeta function is defined for $\mathrm{Re}(s)>1$ and $\mathrm{Re}(a)>0$ by | + | __NOTOC__ |
| − | $$\zeta( | + | The Hurwitz zeta function is a generalization of the [[Riemann zeta]] function defined initially for $\mathrm{Re}(s)>1$ and $\mathrm{Re}(a)>0$ by |
| + | $$\zeta(z,q)= \displaystyle\sum_{k=0}^{\infty} \dfrac{1}{(k+q)^z}.$$ | ||
=Properties= | =Properties= | ||
| − | < | + | [[Hurwitz zeta absolute convergence]]<br /> |
| − | < | + | [[Relationship between Hurwitz zeta and gamma function]]<br /> |
| − | + | [[Relation between polygamma and Hurwitz zeta]]<br /> | |
| − | + | [[Bernoulli polynomial and Hurwitz zeta]]<br /> | |
| − | </ | + | [[Catalan's constant using Hurwitz zeta]]<br /> |
| − | </ | ||
| − | + | =See Also= | |
| − | + | [[Riemann zeta]]<br /> | |
| − | |||
| − | |||
| − | |||
| − | </ | ||
| − | + | =References= | |
| − | + | [[Category:SpecialFunction]] | |
| − | |||
Latest revision as of 01:27, 21 December 2016
The Hurwitz zeta function is a generalization of the Riemann zeta function defined initially for $\mathrm{Re}(s)>1$ and $\mathrm{Re}(a)>0$ by $$\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
