The notation is often used as a shorthand for , analogous to for .
All polylogarithmic functions of are 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).
- Black, Paul E. (2004-12-17). "polylogarithmic". Dictionary of Algorithms and Data Structures. U.S. National Institute of Standards and Technology. Retrieved 2010-01-10.