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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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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. | ||
:<math>\frac{n!}{2πi}\oint\frac{f(z)}{(z-p)^{n+1}}dz=f^{(n)}(p)</math> | |||
If we use this to provide the definition of a derivative at a point, then we can construct a Maclaurin formula f(z) using the derivatives in the coefficients of the terms. | If we use this to provide the definition of a derivative at a point, then we can construct a Maclaurin formula f(z) using the derivatives in the coefficients of the terms. | ||