Difference between revisions of "Errata: Missing factor of 2 pi in residue formula for proof of Theorem 9.3"

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{{errata page
 
{{errata page
| chapter =  
+
| chapter = Frequency Domain Analysis
| page =  
+
| page = 278
| line =  
+
| line = 3
| contributor = R. M. Murray
+
| contributor = L. Xiong
| date =  
+
| date = 30 Dec 08
 
| rev = 2.10a
 
| rev = 2.10a
 
| version = First printing
 
| version = First printing
 
| text =  
 
| text =  
 +
The formula for the residue has a divisor of <math>2 \pi i</math> that is missing in the proof of Theorem 9.3.  The proper formula for the sum of the residues due to the poles and zeros is
 +
<center><amsmath>
 +
  Z - P = \frac{1}{2 \pi i} \int_\Gamma \frac{f'(z)}{f(z)}\, dz
 +
    = \frac{1}{2 \pi i} \int_\Gamma \frac{d}{dz} \log{f(z)}\, dz
 +
    = \frac{1}{2 \pi i} \Delta_\Gamma\log{f(z)}.
 +
</amsmath></center>
 
}}
 
}}

Latest revision as of 18:45, 1 January 2009

Return to Errata page

Location: page 278, line 3

The formula for the residue has a divisor of that is missing in the proof of Theorem 9.3. The proper formula for the sum of the residues due to the poles and zeros is

math

(Contributed by L. Xiong, 30 Dec 08)