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:
“Oh Sleep! it is a gentle thing,
Beloved from pole to pole!
To Mary Queen the praise be given!
She sent the gentle sleep from Heaven,
That slid into my soul.”
—Samuel Taylor Coleridge (1772–1834)
“For me being a poet is a job rather than an activity. I feel I have a function in society, neither more nor less meaningful than any other simple job. I feel it is part of my work to make poetry more accessible to people who have had their rights withdrawn from them.”
—Jeni Couzyn (b. 1942)
“Specialization is a feature of every complex organization, be it social or natural, a school system, garden, book, or mammalian body.”
—Catharine R. Stimpson (b. 1936)
“A large city cannot be experientially known; its life is too manifold for any individual to be able to participate in it.”
—Aldous Huxley (1894–1963)