Flat Function
In mathematics, especially real analysis, a flat function is a smooth function f : \mathbb \to \mathbb all of whose derivatives vanish (mathematics), vanish at a given point x_0 \in \mathbb. The flat functions are, in some sense, the antitheses of the analytic functions. An analytic function f : \mathbb \to \mathbb is given by a convergent series, convergent power series close to some point x_0 \in \mathbb: :f(x) \sim \lim_ \sum_^n \frac (x-x_0)^k . In the case of a flat function, all derivatives vanish at x_0 \in \mathbb, i.e. f^(x_0) = 0 for all k \in \mathbb. This means that a meaningful Taylor series expansion in a neighbourhood (mathematics), neighbourhood of x_0 is impossible. In the language of Taylor's_theorem#Statement, Taylor's theorem, the non-constant part of the function always lies in the remainder R_n(x) for all n \in \mathbb. The function need not be flat at just one point. Trivially, constant functions on \mathbb are flat everywhere. But there are also other, less ...
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FBN Exp(-1x2)
FBN may refer to: Broadcasting * Faith Broadcasting Network, an American Christian television network * Fox Business Network, an American cable television network * Fundamental Broadcasting Network, an American Christian radio network Other uses

*Farmers Business Network, a farmer-to-farmer network and e-commerce platform *Federal Bureau of Narcotics, a former agency of the United States Department of the Treasury *Feminist Bookstore News, a trade publication for feminist bookstores * Fibrillin * First Bank of Nigeria {{disambiguation ...
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