- #1
WannaBe22
- 76
- 0
Homework Statement
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]
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!
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]
Homework Equations
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!