Some tight polynomial-exponential lower bounds for an exponential function

Christophe Chesneau (1)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme

This note is devoted to new sharp lower bounds for exp(x^2). We first introduce and study a new lower bound defined with polynomial of degree 2 and exponential (or hyperbolic) functions. Then we propose two improvements of this lower bound by using two different approaches; the first approach consists in adding well-chosen polynomial term to it, whereas the second approach aims to transform it for large values of |x|. We show that they are better to well-known lower bounds. The analytic results are supported by some numerical studies and graphics. A part of the study is devoted to some integral methods having the ability to generate new lower bounds for exp(x^2).

Mots clés: Algebraic bounds; Exponential function

Domaines: Analyse classique [math.CA]

Christophe Chesneau. Some tight polynomial-exponential lower bounds for an exponential function. 2018. ⟨hal-01680624v1⟩