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 2π 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 (Juli 2006), "A note on an identity of the gamma function and Stirling's formula", Real Analysis Exchange, 32 (1): 267–271, MR 2329236
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Pranala luar
Wikimedia Commons memiliki media mengenai Stirling's approximation.
- 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
- (Inggris)Stirling's approximation di PlanetMath.