# Polylogarithmic

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

[itex]a_k \log^k(n) + \cdots + a_1 \log(n) + a_0.[itex]

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

All polylogarithmic functions are

[itex] P_l(x) = o(x^\epsilon)\,[itex]

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

Not to be confused with polylogarithms.

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