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OPTIMAL POLYNOMIAL LOWER BOUNDS FOR THE EXPONENTIAL FUNCTION

  • Received : 2007.07.26
  • Published : 2007.12.25

Abstract

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 $p(x)\;\leq\;p_n(x)$.

Keywords

bounds;polynomials;the exponential function

References

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Cited by

  1. ON SOME UPPER BOUNDS OF THE EXPONENTIAL FUNCTION vol.30, pp.2, 2008, https://doi.org/10.5831/HMJ.2008.30.2.323