B.21 ZETA FUNCTION
Definition: Riemann Zeta Function The Riemann zeta function is
(B.115) 
where 
is a complex variable.
This series converges provided Re(s) = σ > 1. Figure B.18 shows a plot of 
for real values of s, which converges to zero for σ <0, converges to 1 for σ > 0, and has a pole at s = 1. The zeta function is used in the pmf of the zeta random variable with real-valued 
, which is a scale parameter of the distribution.
Figure B.18 Zeta function 
for real-valued s.
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