stirling limit | Mathematics | Page 1

hexed sky Jan 20, 2023, 3:10 AM

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can anyone help me with this outcome using stirling's?

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frail valley Jan 20, 2023, 6:42 AM

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$$\frac{(2n)!\sqrt{n}}{2^{2n}(n!)^2} \sim \frac{\sqrt{2\pi \cdot 2n} \left( \frac{2n}e\right)^{2n}\cdot \sqrt{n}}{2^{2n}\cdot 2\pi n \left(\frac ne\right)^{2n}}$$

gloomy yokeBOT Jan 20, 2023, 6:42 AM

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k12byda5h

frail valley Jan 20, 2023, 6:43 AM

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$$\sim \frac{2n\sqrt{\pi} }{2\pi n} = ...$$

gloomy yokeBOT Jan 20, 2023, 6:43 AM

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k12byda5h

#stirling limit