两个包含Gamma函数的对数完全单调函数及其应用

Logarithmically complete monotonicity of two specific functions involving Gamma function and applications

通过对两个包含Gamma函数的特殊函数的对数完全单调性的证明,给出了一个新的关于Γ(x+1)的不等式,由此给出了一个关于n!的新估计,并将该估计与已有文献结果进行了比较.最后,基于这个新估计,提出了一个关于n!的最佳不等式的猜想.

In the article,the logarithmically complete monotonicity of two specific functions involving Gamma function was proved.Thus,a new inequality aboutΓ（x＋1）was obtained.And then,a double inequality about factorial n was proposed and compared with the existing conclusions.Lastly,a best conjecture was made on the new estimate.