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Use 5 factor Stirling's Series

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This commit is contained in:
John Scipione 2014-01-17 18:12:46 -05:00
parent fb4dcb4965
commit 261bdbab6d
1 changed files with 6 additions and 4 deletions
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10
src/kits/shared/ExpressionParser.cpp
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@ -712,12 +712,14 @@ ExpressionParser::_ParseFactorial(MAPM value)
if (value < 1000)
return value.factorial();
else {
// Use Stirling's approximation (with extra term)
// http://hyperphysics.phy-astr.gsu.edu/hbase/math/stirling.html
// n! ≈ (n/e)^n * sqrt(2πn) * (1 + (1/12n))
// Use Stirling's approximation (5 term expansion)
// http://en.wikipedia.org/wiki/Stirling%27s_approximation
return value.pow(value) / value.exp()
* (MAPM(2) * MAPM(MM_PI) * value).sqrt()
* (MAPM(1) + (MAPM(1) / (MAPM(12) * value)));
* (MAPM(1) + (MAPM(1) / (MAPM(12) * value))
+ (MAPM(1) / (MAPM(288) * value.pow(2)))
- (MAPM(139) / (MAPM(51840) * value.pow(3)))
- (MAPM(571) / (MAPM(2488320) * value.pow(4))));
}
}