J. The formula is a modification of Stirling's approximation, and has the form (+) = (+) + − − (+ ∑ = − + + ())where a is an arbitrary positive integer and the coefficients are given by but the last term may usually be neglected so that a working approximation is. Stirling’s Approximation and Binomial, Poisson and Gaussian distributions AF 30/7/2014. In mathematics, Stirling's approximation (or Stirling's formula) is an approximation for large factorials. Knar's formula = Z 1 0 xne xdx; which can be veriﬁed by induction, using an integration by parts to reduce the power x nto x 1. Formally, it states:

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