let be a continuous function. Let . Prove that there is a real analytic function such that for all .

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- Apr 18th 2010, 01:13 PMArchianalytic function
let be a continuous function. Let . Prove that there is a real analytic function such that for all .

- Apr 18th 2010, 01:43 PMOpalg
You can even find a polynomial that will do this (that is the Weierstrass approximation theorem). A concrete way to construct a polynomial that approximates a given continuous function to any desired degree of accuracy is to use Bernstein polynomials.

- Apr 18th 2010, 05:28 PMArchi
can i just say it is proven by weierstrass approximation theorem? or do i have to actually show the proof ? i am not sure how to even start. whould u guide me?