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'''NEWS FLASH:''' The due date for HWK 8 has been extended to Monday, Nov. 9 | '''NEWS FLASH:''' The due date for HWK 8 has been extended to Monday, Nov. 9 | ||
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| + | 'Hint for V.16.1:' We know that | ||
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| + | <math>f(z)=\sum_{n=0}^\infty z^n=\frac{1}{1-z}</math> | ||
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| + | if <math>|z|<1</math>. Notice that | ||
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| + | <math>f'(z)=\sum_{n=1}^\infty nz^{n-1}</math>, | ||
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| + | and | ||
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| + | <math>f''(z)=\sum_{n=2}^\infty n(n-1)z^{n-2}</math>. | ||
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| + | What are the power series for <math>zf'(z)</math> and <math>z^f''(z)</math>? How can you combine these to get the series in the question? --[[User:Bell|Steve Bell]] | ||
Revision as of 11:39, 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^f''(z) $? How can you combine these to get the series in the question? --Steve Bell
