Polylogarithmic function

A polylogarithmic function in n is a polynomial in the logarithm of n,

$a_{k}\log ^{k}(n)+\cdots +a_{1}\log(n)+a_{0}.$

In computer science, polylogarithmic functions occur as the order of memory used by some algorithms (e.g., "it has polylogarithmic order").

All polylogarithmic functions are

$P_{l}(x)=o(x^{\epsilon })\,$

for every exponent ε > 0 (for the meaning of this symbol, see small o notation), that is, a polylogarithmic function grows slower than any positive exponent.

Not to be confused with polylogarithms.