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 .
Read more about this topic: Pole (complex Analysis)
Famous quotes containing the words pole, function, complex and/or manifold:
“The discovery of the North Pole is one of those realities which could not be avoided. It is the wages which human perseverance pays itself when it thinks that something is taking too long. The world needed a discoverer of the North Pole, and in all areas of social activity, merit was less important here than opportunity.”
—Karl Kraus (1874–1936)
“The function of muscle is to pull and not to push, except in the case of the genitals and the tongue.”
—Leonardo Da Vinci (1425–1519)
“What we do is as American as lynch mobs. America has always been a complex place.”
—Jerry Garcia (1942–1995)
“The Lord wrote it all down on the little slate
Of the baby tortoise.
Outward and visible indication of the plan within,
The complex, manifold involvedness of an individual creature”
—D.H. (David Herbert)