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Terminology►The expansion (5.11.1) is called Stirling’s series (Whittaker and Watson (1927, §12.33)), whereas the expansion (5.11.3), or sometimes just its leading term, is known as Stirling’s formula (Abramowitz and Stegun (1964, §6.1), Olver (1997b, p. 88)). …
In many cases, the links from mathematical symbols to their definitions were corrected or improved. These links were also enhanced with ‘tooltip’ feedback, where supported by the user’s browser.
In Equations (15.6.1)–(15.6.9), the Olver hypergeometric function , previously omitted from the left-hand sides to make the formulas more concise, has been added. In Equations (15.6.1)–(15.6.5), (15.6.7)–(15.6.9), the constraint has been added. In (15.6.6), the constraint has been added. In Section 15.6 Integral Representations, the sentence immediately following (15.6.9), “These representations are valid when , except (15.6.6) which holds for .”, has been removed.
Additional keywords are being added to formulas (an ongoing project); these are visible in the associated ‘info boxes’ linked to the icons to the right of each formula, and provide better search capabilities.
Previously this formula was expressed as an equality. Since this formula expresses an asymptotic expansion, it has been corrected by using instead an relation.
Reported by Gergő Nemes on 2019-01-29
Originally the Stirling number was given incorrectly as 6327. The correct number is 63273.
Reported 2013-11-25 by Svante Janson.
The formulas in these subsections are valid only for . No conditions on were given originally.
Reported 2010-10-18 by Andreas Kurt Richter.