OPTIMAL POLYNOMIAL LOWER BOUNDS FOR THE EXPONENTIAL FUNCTION
Jaegug Bae · Honam Mathematical Journal · 2007
In this paper, for each natural number n, we construct a polynomial $p_n$ (x) of degree n so that $p_n(x)\;\leq\;p_{n+1}(x)\;\leq\;e^x$ for $x\;\geq\;-1$ . These polynomials are optimal in the sense that if p(x) is a polynomial of degree n with $p_{n-l}(x)\;\leq\;p(x)\;\leq\;e^x$ , then $p(x)\;\leq\;p_n(x)$ .