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• 13:37, 30 January 2026 T talk contribs created page File:FactorialAsymPlotT.png ({{oq|FactorialAsymPlotT.png|FactorialAsymPlotT.png ‎(708 × 487 pixels, file size: 48 KB, MIME type: image/png) |}} Explicit plot of Factorial and its primitive Stirling asymptotic \[ A(x)=\sqrt{2\pi x} \exp\!\big(\log(x/\mathrm e)\ x\big) \] The green curve shows he Residual \[ R(x) = x! - A(x) \] The blue curve shoes the Logarithmic residual \[ r(x) = \log(x!) - \log(A(x)) \] A large \(x\) the residual \( R(x) \) becomes infinite, but \[ \lim_{x\to +\infty} r(x)=0 \]...)
• 13:37, 30 January 2026 T talk contribs uploaded File:FactorialAsymPlotT.png ({{oq|FactorialAsymPlotT.png|FactorialAsymPlotT.png ‎(708 × 487 pixels, file size: 48 KB, MIME type: image/png) |}} Explicit plot of Factorial and its primitive Stirling asymptotic \[ A(x)=\sqrt{2\pi x} \exp\!\big(\log(x/\mathrm e)\ x\big) \] The green curve shows he Residual \[ R(x) = x! - A(x) \] The blue curve shoes the Logarithmic residual \[ r(x) = \log(x!) - \log(A(x)) \] A large \(x\) the residual \( R(x) \) becomes infinite, but \[ \lim_{x\to +\infty} r(x)=0 \]...)