Question

求证 函数 多项式有界（注：以“┌”“┐”表示向上取整符号,以“lgn”表示以2为底n的对数,”表示阶乘符号） 问：函数

Answer 1

┌lgn┐!cannot be upper-bounded by polynomials of n,while ┌lg（lgn）┐!can be bounded.This can be derived by simply applying Stirling's asymptotic approximation of factorials.