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:
“O, withered is the garland of the war,
The soldier’s pole is fallen!”
—William Shakespeare (1564–1616)
“To make us feel small in the right way is a function of art; men can only make us feel small in the wrong way.”
—E.M. (Edward Morgan)
“Power is not an institution, and not a structure; neither is it a certain strength we are endowed with; it is the name that one attributes to a complex strategical situation in a particular society.”
—Michel Foucault (1926–1984)
“They had met, and included in their meeting the thrust of the manifold grass stems, the cry of the peewit, the wheel of the stars.”
—D.H. (David Herbert)