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user434058
user434058
0
Consider the function $f_r(s) + v = (\sum_{n=1}^{\infty} \frac{1}{n + n^s + r}) + v $ for real $r,v$ and complex $s$.
( with respect to variable $s$ and fixed $r,v$)
I wonder how this function looks like and behaves with respect to $s$.
Where are the poles and zero's ? Is there a critical line l...
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Consider a nondecreasing infinite sequence of positive integers that starts with $1$ : $a_n$
( so $a_1 = 1$ )
Example $a_1 = 1 , a_2 = 3 , a_3 = 3 , a_4 = 7 , a_5 = 12,... $
Now consider $f(s) = \sum_{n=1}^{\infty} \frac{1}{a_i^s} $
How do I know if I can do analytic continuation so that $f(s)$ w...
Define a function $F(s)$ by:
$$F(s)=\sum_{n=0}^{\infty}(\sqrt n+1/3)^{-s}$$
Is there a closed form expression for the analytic continuation of $F(s)$ to $F(-s)$?
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