(adsbygoogle = window.adsbygoogle || []).push({}); The problem statement, all variables and given/known data

Find the analytic regions of the next functions:

A. [tex] f(z)=\sum_{n=1}^{\infty} [ \frac{z(z+n)}{n}]^n [/tex]

B. [tex] f(z)=\sum_{n=1}^{\infty} 2^{-n^2 z} \cdot n^n [/tex]

2. Relevant equations

3. The attempt at a solution

In the first one: I've tried writing : [tex] f(z)= \sum \frac{z^{2n}}{n^n} + \sum z^n [/tex]

and the second element in the sum converges iff |z|<1... Is it enough?

About B: We can write this series as: [tex] \sum [ \frac{n}{2^{nz}}]^n [/tex] ... But I don't think it helps us...

Hope you'll be able to help me

TNX!

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# Complex Analysis-Series

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