Polylogarithmic function

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${\displaystyle a_{k}\log ^{k}(n)+\cdots +a_{1}\log(n)+a_{0}.\,}$
All polylogarithmic functions of ${\displaystyle n}$ are ${\displaystyle o(n^{\varepsilon })\,}$ 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).