Hurwitz zeta

From specialfunctionswiki
Revision as of 01:27, 21 December 2016 by Tom (talk | contribs)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

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