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146 lines
1.4 KiB
146 lines
1.4 KiB
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Exercise 3.61: Let
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S
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be a power series
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(Exercise 3.59) whose constant term is 1. Suppose we want to find the
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power series
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1
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/
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S
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, that is, the series
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X
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such that
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S
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X
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=
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1
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.
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Write
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S
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=
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1
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+
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S
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R
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where
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S
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R
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is the part of
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S
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after the
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constant term. Then we can solve for
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X
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as follows:
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S
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⋅
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X
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=
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1
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,
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(
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1
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+
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S
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R
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)
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⋅
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X
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=
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1
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,
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X
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+
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S
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R
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⋅
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X
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=
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1
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,
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X
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=
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1
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−
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S
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R
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⋅
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X
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.
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In other words,
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X
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is the power series whose constant term is 1 and whose
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higher-order terms are given by the negative of
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S
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R
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times
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X
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. Use
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this idea to write a procedure invert-unit-series that computes
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1
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/
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S
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for a power series
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S
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with constant term 1. You will need to use
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mul-series from Exercise 3.60.
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