Polylogarithmic function

A polylogarithmic function in "n" is a polynomial in the logarithm of "n",
The notation formula_2 is often used as a shorthand for formula_3, analogous to formula_4 for formula_5.
In computer science, polylogarithmic functions occur as the order of time or memory used by some algorithms (e.g., "it has polylogarithmic order").
All polylogarithmic functions of formula_6 are formula_7 for every exponent "ε" > 0 (for the meaning of this symbol, see small o notation), that is, a polylogarithmic function grows more slowly than any positive exponent. This observation is the basis for the soft O notation Õ("n").