Difference between revisions of "Q-zeta"
From specialfunctionswiki
| Line 1: | Line 1: | ||
Let $|q|<1$. The $q$-zeta function $\zeta_q \colon \mathbb{C} \times (0,1] \rightarrow \mathbb{C}$ is defined for $\mathrm{Re}(z)>1$ by | Let $|q|<1$. The $q$-zeta function $\zeta_q \colon \mathbb{C} \times (0,1] \rightarrow \mathbb{C}$ is defined for $\mathrm{Re}(z)>1$ by | ||
| − | $$\zeta_q(z | + | $$\zeta_q(z)=\displaystyle\sum_{k=0}^{\infty} \dfrac{q^{-k}}{(q^{-k}[k])^z},$$ |
where $[k]$ denotes a [[q-number|$q$-number]]. | where $[k]$ denotes a [[q-number|$q$-number]]. | ||
Revision as of 17:47, 11 February 2018
Let $|q|<1$. The $q$-zeta function $\zeta_q \colon \mathbb{C} \times (0,1] \rightarrow \mathbb{C}$ is defined for $\mathrm{Re}(z)>1$ by $$\zeta_q(z)=\displaystyle\sum_{k=0}^{\infty} \dfrac{q^{-k}}{(q^{-k}[k])^z},$$ where $[k]$ denotes a $q$-number.
