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  
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__NOTOC__
$$\zeta(s,a)= \displaystyle\sum_{n=0}^{\infty} \dfrac{1}{(n+a)^s}.$$
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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  
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$$\zeta(z,q)= \displaystyle\sum_{k=0}^{\infty} \dfrac{1}{(k+q)^z}.$$
  
 
=Properties=
 
=Properties=
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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=
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[[Riemann zeta]]<br />
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=References=
  
 
[[Category:SpecialFunction]]
 
[[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

See Also

Riemann zeta

References