Gamma函数和Psi函数的单调性质与不等式

Monotonicity properties and inequalities of gamma and psi functions

给出了一族含有Gamma函数的对数完全单调函数,建立了一些含有Psi函数和Poly-amma函数的不等式,推广并改进了一些已有的结果.另外,给出了函数x2ψx+1/2-ψ(x)-2/1x的单调递增性的新证明.

A class of logarithmically completely monotonic function involving the gamma function is presented, and some inequalities involving the psi and polygamma functions are established. Theorems are generalized and some known results are improved. Finaly, a new proof of the increasingness for the function x^2[ψ（x＋2^-1）-ψ（x）-2x^-1]is given.