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Stirling’s formula
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Stirling’s formula

mathematics
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Also known as: Stirling’s approximation
Written by
William L. Hosch
William L. Hosch was an editor at Encyclopædia Britannica.
William L. Hosch
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The Editors of Encyclopaedia Britannica
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Also called:
Stirling’s approximation
Key People:
Abraham de Moivre
James Stirling
Related Topics:
factorial
See all related content

Stirling’s formula, in analysis, a method for approximating the value of large factorials (written n!; e.g., 4! = 1 × 2 × 3 × 4 = 24) that uses the mathematical constants e (the base of the natural logarithm) and π. The formula is given by Stirling's Formula

The Scottish mathematician James Stirling published his formula in Methodus Differentialis sive Tractatus de Summatione et Interpolatione Serierum Infinitarum (1730; “Differential Method with a Tract on Summation and Interpolation of Infinite Series”), a treatise on infinite series, summation, interpolation, and quadrature.

For practical computations, Stirling’s approximation, which can be obtained from his formula, is more useful: lnn! ≅ nlnn − n, where ln is the natural logarithm. Using existing logarithm tables, this form greatly facilitated the solution of otherwise tedious computations in astronomy and navigation.

William L. Hosch