Stirling's approximation: Difference between revisions
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Carl McBride (talk | contribs) m (New page: James Stirling (1692-1770, Scotland) :<math>\left.\ln N!\right. = \ln 1 + \ln 2 + \ln 3 + ... + \ln N</math> :<math> ~= \sum_{k=1}^N \ln k</math> :<math>~\approx \int_1^N \ln x dx</ma...) |
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:<math>\ln N! \approx N \ln N -N</math> | :<math>\ln N! \approx N \ln N -N</math> | ||
[[Category: Mathematics]] | |||
Revision as of 12:56, 27 February 2007
James Stirling (1692-1770, Scotland)
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left.\ln N!\right. = \ln 1 + \ln 2 + \ln 3 + ... + \ln N}
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle ~= \sum_{k=1}^N \ln k}
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle ~\approx \int_1^N \ln x dx}
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle ~= \left[ x \ln x - x \right]_1^N}
- Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle ~=N\ln N-N+1}
Thus, for large N
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \ln N! \approx N \ln N -N}