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 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
sunting- ^ 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 does not entitle him to claim the theorem, [...]
Bacaan lebih lanjut
sunting- 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 : 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
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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.
