Simple Search

Query:

Enter a query and click »Search«...

Format:

Display: entries per page entries

Zbl 1213.33007
Mortici, Cristinel
A new Stirling series as continued fraction. (English)
[J] Numer. Algorithms 56, No. 1, 17-26 (2011). ISSN 1017-1398; ISSN 1572-9265/e

Summary: We have the well-known Stirling's formula $n!\sim \sqrt{2\pi n}(\frac ne)^n$. This formula is the first approximation of the stirling series: $$n~\sim\sqrt{2\pi n} \bigg(\frac ne\bigg)^n \exp (\bigg( \frac{1}{12n}- \frac{1}{360n^3}+ \frac{1}{1260^{n^5}}- \cdots\bigg).$$ The author has formulated the following new Stirling series as a continued fraction $$ n! \sim \sqrt{2\pi n}\bigg( \frac{n}{e}\bigg)^n\exp \cfrac1\\ 12n+\cfrac \frac25\\ n+ \cfrac \frac{53}{210}\\ n+\cfrac \frac{195}{371}\\ n+\cfrac \frac{22999}{22737}\\ n+\ddots \endcfrac $$

MSC 2000:: *33B15 Gamma-functions, etc.
11B73 Bell and Stirling numbers
40A15 Convergence of continued fractions
41A60 Asymptotic problems in approximation

Keywords: Stirling formula; rate of convergence; approximations; asymptotic expansions

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Simple Search

Zentralblatt MATH Berlin [Germany]