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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]] | 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]] | ||
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| + | Does anybody know how to attack problem 10.2? Also for problem 8.1, I just Taylor expanded the function w.r.t to z, I am not sure if that is right since the book doesn't mention anything about Taylor's theorem. Did anybody do it another way? | ||
| + | --Adrian Delancy | ||
Revision as of 06:32, 8 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
Does anybody know how to attack problem 10.2? Also for problem 8.1, I just Taylor expanded the function w.r.t to z, I am not sure if that is right since the book doesn't mention anything about Taylor's theorem. Did anybody do it another way? --Adrian Delancy
