About: Stirling's approximation

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In mathematics, Stirling's approximation (or Stirling's formula) is an approximation for factorials. It is a good approximation, leading to accurate results even for small values of . It is named after James Stirling, though a related but less precise result was first stated by Abraham de Moivre. The version of the formula typically used in applications is

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rdfs:label	Stirling's approximation (en)
rdfs:comment	In mathematics, Stirling's approximation (or Stirling's formula) is an approximation for factorials. It is a good approximation, leading to accurate results even for small values of . It is named after James Stirling, though a related but less precise result was first stated by Abraham de Moivre. The version of the formula typically used in applications is (en)
sameAs	Stirling's approximation Stirling's approximation
dbp:wikiPageUsesTemplate	dbt:= dbt:Citation dbt:Clarify dbt:Commons_category dbt:Math dbt:MathWorld dbt:Mvar dbt:R dbt:Reflist dbt:Sfrac dbt:Short_description dbt:Abs dbt:OEIS_link dbt:Calculus_topics dbt:PlanetMath dbt:SpringerEOM
Subject	Approximations Asymptotic analysis Theorems in analysis Gamma and related functions Analytic number theory
prov:wasDerivedFrom	http://en.wikipedia.org/wiki/Stirling's_approximation?oldid=1068285162&ns=0
Wikipage page ID	151783 (xsd:integer)
page length (characters) of wiki page	23699 (xsd:nonNegativeInteger)
Wikipage revision ID	1068285162 (xsd:integer)
has abstract	In mathematics, Stirling's approximation (or Stirling's formula) is an approximation for factorials. It is a good approximation, leading to accurate results even for small values of . It is named after James Stirling, though a related but less precise result was first stated by Abraham de Moivre. The version of the formula typically used in applications is (in Big Theta notation, as ), or, by changing the base of the logarithm (for instance in the worst-case lower bound for comparison sorting), Specifying the constant in the O(ln n) error term gives 1/2ln(2πn), yielding the more precise formula:where the sign ~ means that the two quantities are asymptotic: their ratio tends to 1 as tends to infinity. The following version of the bound holds for all , rather than only asymptotically: (en)
foaf:isPrimaryTopicOf	http://en.wikipedia.org/wiki/Stirling's_approximation
is Wikipage redirect of	Log(n!) Approximation Sterling Approximation Stirling's Approximation Stirlings approximation Sterling's approximation Sterling Formula Stirling's Stirling's Formula Stirling's formula Stirling's series Stirling's theorem Stirling approximation Stirling formula Stirling series
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