Pole of A Function On A Complex Manifold
In general, having a function that is holomorphic in a neighborhood, of the point, in the complex manifold M, it is said that f has a pole at a of order n if, having a chart, the function has a pole of order n at (which can be taken as being zero if a convenient choice of the chart is made). ] The pole at infinity is the simplest nontrivial example of this definition in which M is taken to be the Riemann sphere and the chart is taken to be .
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