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<math>f''(z)=\sum_{n=2}^\infty n(n-1)z^{n-2}</math>. | <math>f''(z)=\sum_{n=2}^\infty n(n-1)z^{n-2}</math>. | ||
| − | What are the power series for <math>zf'(z)</math> and <math>z^ | + | What are the power series for <math>zf'(z)</math> and <math>z^2f''(z)</math>? How can you combine these to get the series in the question? --[[User:Bell|Steve Bell]] |
Revision as of 11:40, 6 November 2009
Homework 8
NEWS FLASH: The due date for HWK 8 has been extended to Monday, Nov. 9
Hint for V.16.1: We know that
$ f(z)=\sum_{n=0}^\infty z^n=\frac{1}{1-z} $
if $ |z|<1 $. Notice that
$ f'(z)=\sum_{n=1}^\infty nz^{n-1} $,
and
$ f''(z)=\sum_{n=2}^\infty n(n-1)z^{n-2} $.
What are the power series for $ zf'(z) $ and $ z^2f''(z) $? How can you combine these to get the series in the question? --Steve Bell
