Rumus Stirling

Dalam matematika, aproksimasi Stirling' (atau rumus Stirling) adalah aproksimasi asimtotik untuk faktorial. Ini adalah aproksimasi yang baik, yang menghasilkan hasil yang akurat bahkan untuk nilai $n$ yang kecil. Rumus ini dinamai menurut James Stirling, meskipun hasil yang terkait tetapi kurang tepat pertama kali dinyatakan oleh Abraham de Moivre.^[1]^[2]^[3]

Referensi

^ Dutka, Jacques (1991), "The early history of the factorial function", Archive for History of Exact Sciences, 43 (3): 225–249, doi:10.1007/BF00389433, S2CID 122237769
^ Le Cam, L. (1986), "The central limit theorem around 1935", Statistical Science, 1 (1): 78–96, doi:10.1214/ss/1177013818, JSTOR 2245503, MR 0833276; see p. 81, "The result, obtained using a formula originally proved by de Moivre but now called Stirling's formula, occurs in his 'Doctrine of Chances' of 1733."
^ Pearson, Karl (1924), "Historical note on the origin of the normal curve of errors", Biometrika, 16 (3/4): 402–404 [p. 403], doi:10.2307/2331714, JSTOR 2331714, I consider that the fact that Stirling showed that De Moivre's arithmetical constant was ${\sqrt {2\pi }}$ does not entitle him to claim the theorem, [...]

Bacaan lebih lanjut

Abramowitz, M. & Stegun, I. (2002), Handbook of Mathematical Functions
Paris, R. B. & Kaminski, D. (2001), Asymptotics and Mellin–Barnes Integrals, New York: Cambridge University Press, ISBN 978-0-521-79001-7
Whittaker, E. T. & Watson, G. N. (1996), A Course in Modern Analysis (Edisi 4th), New York: Cambridge University Press, ISBN 978-0-521-58807-2
Romik, Dan (2000), "Stirling's approximation for $n!$ : the ultimate short proof?", The American Mathematical Monthly, 107 (6): 556–557, doi:10.2307/2589351, JSTOR 2589351, MR 1767064
Li, Yuan-Chuan (July 2006), "A note on an identity of the gamma function and Stirling's formula", Real Analysis Exchange, 32 (1): 267–271, MR 2329236

Pranala luar

Hazewinkel, Michiel, ed. (2001) [1994], "Stirling_formula", Encyclopedia of Mathematics, Springer Science+Business Media B.V. / Kluwer Academic Publishers, ISBN 978-1-55608-010-4
Peter Luschny, Approximation formulas for the factorial function n!
(Inggris) Weisstein, Eric W., "Stirling's Approximation", MathWorld
Stirling's approximation di PlanetMath.

[dutka-1] Dutka, Jacques (1991), "The early history of the factorial function", Archive for History of Exact Sciences, 43 (3): 225–249, doi:10.1007/BF00389433, S2CID 122237769

[LeCam1986-2] Le Cam, L. (1986), "The central limit theorem around 1935", Statistical Science, 1 (1): 78–96, doi:10.1214/ss/1177013818, JSTOR 2245503, MR 0833276; see p. 81, "The result, obtained using a formula originally proved by de Moivre but now called Stirling's formula, occurs in his 'Doctrine of Chances' of 1733."

[Pearson1924-3] Pearson, Karl (1924), "Historical note on the origin of the normal curve of errors", Biometrika, 16 (3/4): 402–404 [p. 403], doi:10.2307/2331714, JSTOR 2331714, I consider that the fact that Stirling showed that De Moivre's arithmetical constant was ${\sqrt {2\pi }}$ does not entitle him to claim the theorem, [...]

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