Difference between revisions of "Hurwitz zeta"
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(Created page with "The Hurwitz zeta function is defined for $\Re(s)>1$, $$\zeta(s,a)= \displaystyle\sum_{n=0}^{\infty} \dfrac{1}{(n+a)^s}.$$") |
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| − | The Hurwitz zeta function is defined for $\Re(s)>1$ | + | __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}.$$ | ||
| + | |||
| + | =Properties= | ||
| + | [[Hurwitz zeta absolute convergence]]<br /> | ||
| + | [[Relationship between Hurwitz zeta and gamma function]]<br /> | ||
| + | [[Relation between polygamma and Hurwitz zeta]]<br /> | ||
| + | [[Bernoulli polynomial and Hurwitz zeta]]<br /> | ||
| + | [[Catalan's constant using Hurwitz zeta]]<br /> | ||
| + | |||
| + | =See Also= | ||
| + | [[Riemann zeta]]<br /> | ||
| + | |||
| + | =References= | ||
| + | |||
| + | [[Category:SpecialFunction]] | ||
Latest revision as of 01:27, 21 December 2016
The Hurwitz zeta function is a generalization of the Riemann zeta function defined initially for $\mathrm{Re}(s)>1$ and $\mathrm{Re}(a)>0$ by $$\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
