In mathematics, a polylogarithmic function in n is a polynomial in the logarithm of n,[1] The notation logkn is often used as a shorthand for (log n)k, analogous to sin2θ for (sin θ)2.
In computer science, polylogarithmic functions occur as the order of time for some data structure operations.
[2] All polylogarithmic functions of n are o(nε) 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).
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