Difference between revisions of "The Road to Reality Study Notes"

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=== 7.3 Power series from complex smoothness ===
=== 7.3 Power series from complex smoothness ===
The example in section 7p2 is a particular case for the well-known Cauchy Formula, which allows us to know what the function is doing at the origin (or another general point p) by what it is doing at a set of points surrounding the origin (or the general point p). <math display="block">\frac{1}{2πi}</math>
The example in section 7p2 is a particular case for the well-known Cauchy Formula, which allows us to know what the function is doing at the origin (or another general point p) by what it is doing at a set of points surrounding the origin (or the general point p).  
 
:<math>\frac{1}{2πi}\oint\frac{f(z)}{z-p}dz=f(p)</math>


A higher-order version of this formula allows us to inspect n number of derivatives with the same relationship.
A higher-order version of this formula allows us to inspect n number of derivatives with the same relationship.
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