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Polynomial approximation of an entire function and rate of growth of Taylor coefficients
The best uniform approximation of a function f on [-1,1] by real algebraic polynomials satisfies if and only if ƒ is the restriction to [- 1,1] of an entire function (Bernstein [ 2 ], p. 113, see also [ 12 ], pp. 83–85). For such functions ƒ the rate of …