利用Taylor公式,本文给出关于常数e的一个恒等式及一些双边不等式,利用它们改进了Carleman不等式,同时改进了文献[1,2,3,4,6]的结果.
By using Taylor's formula,an identity on constant and some double inequalities were presented.A strengthened Carleman's inequality was given.The conclusion of literature [1,2,3,4,6] was improved.