Stirlingův vzorec
| Thesis title in Czech: | Stirlingův vzorec |
|---|---|
| Thesis title in English: | Stirling's formula |
| Key words: | faktoriál, aproximace, Abraham de Moivre, James Stirling, mocninné řady, integrál závislý na parametru |
| English key words: | factorial, approximation, Abraham de Moivre, James Stirling, power series, integral depending on a parameter |
| Academic year of topic announcement: | 2015/2016 |
| Thesis type: | Bachelor's thesis |
| Thesis language: | |
| Department: | Department of Mathematics Education (32-KDM) |
| Supervisor: | Mgr. Zdeněk Halas, DiS., Ph.D. |
| Author: | hidden - assigned and confirmed by the Study Dept. |
| Date of registration: | 21.03.2016 |
| Date of assignment: | 27.06.2016 |
| Confirmed by Study dept. on: | 11.07.2016 |
| Guidelines |
| Práce bude obsahovat odvození Stirlingova vzorce. Důraz bude přitom kladen na srozumitelnost a zajímavé matematické postupy.
Následně budou ukázány jednoduché možnosti zpřesnění této aproximace faktoriálu. Text bude doplněn historickými poznámkami. |
| References |
| Fowler D.: The Factorial Function: Stirling’s Formula. Math. Gazette 84(2000), 42-50.
Diaconis P., Freedman D.: An Elementary Proof of Stirling's Formula. American Mathematical Monthly, 93 (1986), No. 2, 123-125. Coleman A. J.: A Simple Proof of Stirling's Formula. American Mathematical Monthly, Vol. 58 (1951), pp. 334-336. Bauer F. L.: Remark on Stirling’s Formulas and on Approximations for the Double Factorial. Mathematical Intelligencer, 28, 2 (2006), 10-21. Batir N.: Inequalities for the gamma function. Arch. Math. (Basel), 91 (2008), 554-563. Dutka J.: The early history of the factorial function. Archive for History of Exact Sciences, September 1991, Volume 43, Issue 3, pp 225-249. Robbins H.: A Remark on Stirling's Formula. MAA, American Mathematical Monthly, Vol. 62, No. 1 (Jan., 1955), pp. 26-29. |