monomocoso
New member
- Joined
- Jan 25, 2012
- Messages
- 31
Let
\(\displaystyle t_i (n)\)
denote the number of factorizations of n into i positive integers. We count factors of 1 and order matters, so for example we can say that 1*3*1, 3*1*1, and 1*1*3 are all factorizations of 3 into 3 ints.
What is the radius of convergence of
\(\displaystyle \displaystyle\sum_{n=1}^{\infty} {t_i (n)z^n }\)
Begin by showing \(\displaystyle i \le t_i (n) \le n^i\)
\(\displaystyle t_i (n)\)
denote the number of factorizations of n into i positive integers. We count factors of 1 and order matters, so for example we can say that 1*3*1, 3*1*1, and 1*1*3 are all factorizations of 3 into 3 ints.
What is the radius of convergence of
\(\displaystyle \displaystyle\sum_{n=1}^{\infty} {t_i (n)z^n }\)
Begin by showing \(\displaystyle i \le t_i (n) \le n^i\)
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