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# Editing Stirling's approximation

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− | '''Stirling's approximation''' is named after the Scottish mathematician James Stirling (1692-1770) | + | '''Stirling's approximation''' is named after the Scottish mathematician James Stirling (1692-1770). |

:<math>\left.\ln N!\right. = \ln 1 + \ln 2 + \ln 3 + ... + \ln N = \sum_{k=1}^N \ln k .</math> | :<math>\left.\ln N!\right. = \ln 1 + \ln 2 + \ln 3 + ... + \ln N = \sum_{k=1}^N \ln k .</math> | ||

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In [[Computer simulation techniques | computer simulations]] the number of atoms or molecules (N) is invariably greater than 100; for N=100 the | In [[Computer simulation techniques | computer simulations]] the number of atoms or molecules (N) is invariably greater than 100; for N=100 the | ||

percentage error is approximately 0.083%. | percentage error is approximately 0.083%. | ||

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==Applications in statistical mechanics== | ==Applications in statistical mechanics== | ||

*[[Ideal gas Helmholtz energy function]] | *[[Ideal gas Helmholtz energy function]] | ||

==References== | ==References== | ||

− | + | #J. Stirling "Methodus differentialis, sive tractatus de summation et interpolation serierum infinitarium", London (1730). English translation by J. Holliday "The Differential Method: A Treatise of the Summation and Interpolation of Infinite Series" (1749) | |

[[Category: Mathematics]] | [[Category: Mathematics]] |