# Burnside formula

The **formula of Burnside** is a formula of mathematical sub-region of the analysis , which the English mathematician William Burnside back. It is closely related to Stirling's formula and, like this, gives an approximation of the factorial function .

## Representation of the formula

Burnside's formula can be given as follows:

## Goodness of approach

Claudi Alsina and Roger B. Nelsen refer in their monograph *Bewitching Evidence* (Springer, 2013) to the fact that Burnside's formula is “approximately twice as accurate as Stirling's formula” and that its derivation “can be derived from approximations for the integral “Wins.

## See also

## literature

- Claudi Alsina, Roger B. Nelsen: Enchanting Evidence: A Journey Through the Elegance of Mathematics . Springer Spectrum , Berlin (among others) 2013, ISBN 978-3-642-34792-4 , p. 269, 306-307 .
- Francis J. Murray : Formulas for Factorial N . In: Mathematics of Computation . tape 39 , 1982, pp. 655–661 ( online copy [PDF]).
- William Burnside : A rapidly convergent series for Log N! In: The Messenger of Mathematics . tape 46 , 1917, pp. 157-159 .