Reflection high-energy electron diffraction: Difference between revisions
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{{Distinguish|Polylogarithm}} | |||
A '''polylogarithmic function''' in ''n'' is a [[polynomial]] in the [[logarithm]] of ''n'', | |||
: <math>a_k \log^k(n) + \cdots + a_1 \log(n) + a_0. \, </math> | |||
In [[computer science]], polylogarithmic functions occur as the [[Big O notation|order]] of [[space complexity|memory used]] by some [[algorithm]]s (e.g., "it has polylogarithmic order"). | |||
All polylogarithmic functions are | |||
= | : <math> P_\ell(x) = o(x^\varepsilon)\,</math> | ||
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]]. | |||
== | == References == | ||
* {{cite web|url=http://xlinux.nist.gov/dads/HTML/polylogarith.html|title=polylogarithmic|last=E. Black|first=Paul|date=2004-12-17|work=Dictionary of Algorithms and Data Structures|publisher=U.S. National Institute of Standards and Technology|accessdate=2010-01-10}} | |||
[[Category:Mathematical analysis]] | |||
[[Category:Polynomials]] | |||
[[Category:Analysis of algorithms]] | |||
{{mathanalysis-stub}} | |||
{{comp-sci-stub}} | |||
Latest revision as of 01:31, 21 January 2014
Template:Distinguish A polylogarithmic function in n is a polynomial in the logarithm of n,
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
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.
References
Template:Mathanalysis-stub
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