A double inequality for tanh x

[摘要] In this paper, we prove that, for $x>0$, $$ \sqrt{1-\exp \biggl(-\frac{x^{2}}{\sqrt{x^{2}+1}} \biggr)}< \tanh x< \sqrt[3]{1-\exp \biggl(- \frac{x^{3}}{\sqrt{x^{3}+1}} \biggr)}. $$This solves an open problem proposed by Ivády.

[学科分类] 电力

[关键词] Inequality;Exponential function;Hyperbolic function