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The Road to Reality Study Notes: Difference between revisions
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→7.3 Power series from complex smoothness
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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 | 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. | ||