- Thread starter
- Moderator
- #1
- Jan 26, 2012
- 995
Thanks again to those who participated in last week's POTW! Here's this week's problem!
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Problem: If $\displaystyle f(x)=\sum_{m=0}^{\infty} c_mx^m$ has positive radius of convergence and $e^{f(x)}= \displaystyle \sum_{n=0}^{\infty} d_n x^n$, show that
\[n d_n = \sum_{i=1}^n i c_i d_{n-i},\qquad n\geq 1.\]
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Remember to read the POTW submission guidelines to find out how to submit your answers!
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Problem: If $\displaystyle f(x)=\sum_{m=0}^{\infty} c_mx^m$ has positive radius of convergence and $e^{f(x)}= \displaystyle \sum_{n=0}^{\infty} d_n x^n$, show that
\[n d_n = \sum_{i=1}^n i c_i d_{n-i},\qquad n\geq 1.\]
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Remember to read the POTW submission guidelines to find out how to submit your answers!