mathematics, Stirling's approximation (or Stirling's formula) is an asymptotic approximation for factorials. It is a good approximation, leading to accurate...

Moivre in 1721, a 1729 letter from James Stirling to de Moivre stating what became known as Stirling's approximation, and work at the same time by Daniel...

accurate approximation can be obtained by using more terms from the asymptotic expansions of ln(Γ(z)) and Γ(z), which are based on Stirling's approximation. Γ...

an approximation for the central term of a binomial expansion. (de Moivre, 1730), p. 99. The roles of de Moivre and Stirling in finding Stirling's approximation...

to the more popular Stirling's approximation for calculating the gamma function with fixed precision. The Lanczos approximation consists of the formula...

{4}{5}}\cdot {\frac {6}{5}}\cdot {\frac {6}{7}}\cdots \end{aligned}}}     Stirling's approximation for the factorial function n ! {\displaystyle n!} asserts that...

and complex integration. Laplace's method can be used to derive Stirling's approximation N ! ≈ 2 π N N N e − N {\displaystyle N!\approx {\sqrt {2\pi N}}N^{N}e^{-N}\...

{\sqrt {2\pi n}}\left({\frac {n}{e}}\right)^{n}} which is known as Stirling's approximation. Equivalently, π = lim n → ∞ e 2 n n ! 2 2 n 2 n + 1 . {\displaystyle...

mathematician. He was nicknamed "The Venetian". The Stirling numbers, Stirling permutations, and Stirling's approximation are named after him. He also proved the...

\sim {\sqrt {2\pi n}}\left({\frac {n}{e}}\right)^{n}} —this is Stirling's approximation Partition function For a positive integer n, the partition function...

given via Stirling's approximation. An upper bound of the same form, with the same leading term as the bound obtained from Stirling's approximation, follows...

constant) Exponential function Hyperbolic angle Hyperbolic function Stirling's approximation Bernoulli numbers See also list of numerical analysis topics Rectangle...

2k selected elements. It follows from the summation formula and Stirling's approximation that, asymptotically, T ( n ) ∼ ( n e ) n / 2 e n ( 4 e ) 1 / 4...

postulate Sierpinski triangle Star of David theorem Stirling number Stirling transform Stirling's approximation Subfactorial Table of Newtonian series Taylor...

Look up Stirling in Wiktionary, the free dictionary. Stirling is a city and former ancient burgh in Scotland. Stirling may also refer to: Stirling's approximation...

the formula in a 1994 paper. The formula is a modification of Stirling's approximation, and has the form Γ ( z + 1 ) = ( z + a ) z + 1 2 e − z − a ( c...

}}\,2^{n-2}\,{\frac {(\Gamma (n/2))^{2}}{\Gamma (n-1)}}} Using Stirling's approximation for Gamma function, we get the following expression for the mean:...

nO(\log n)-O(n)=O(n\log n)} . This can also be readily seen from Stirling's approximation. Amortized time. Brodal and Okasaki describe a technique to reduce...

ψ ( z ) {\displaystyle \psi (z)} denotes the digamma function. Stirling's approximation gives the asymptotic formula B ( x , y ) ∼ 2 π x x − 1 / 2 y y...

may be computed using a generalization of Kummer's theorem. By Stirling's approximation, or equivalently the log-gamma function's asymptotic expansion...

{\displaystyle g_{i}\gg N_{i}} . Under these conditions, we may use Stirling's approximation for the factorial: N ! ≈ N N e − N , {\displaystyle N!\approx N^{N}e^{-N}...

{3}{2}}\right]+{\frac {5}{2}}\end{aligned}}} The derivation uses Stirling's approximation, ln ⁡ N ! ≈ N ln ⁡ N − N {\displaystyle \ln N!\approx N\ln N-N}...

{\displaystyle n\to \infty } . In this case, one may make use of Stirling's approximation to the factorial, and write n ! = 2 π n n n e − n ( 1 + O ( 1 n...

Park. Mathematics portal Binomial approximation Binomial distribution Binomial inverse theorem Stirling's approximation Tannery's theorem Polynomials calculating...

hyperoctahedral groups (signed permutations or symmetries of a hypercube) Stirling's approximation for the factorial can be used to derive an asymptotic equivalent...

Θ ( n log ⁡ n ) {\displaystyle \log(n!)=\Theta (n\log n)} , by Stirling's approximation. They also frequently arise from the recurrence relation T ( n...

{\displaystyle \mu _{g}=-k_{\rm {B}}T\ln(q/N)} , where we use Stirling's approximation. Plugging μ g {\displaystyle \mu _{g}} to the expression of x {\displaystyle...

is the Lambert W function. The formula is found by inverting the Stirling approximation, and so can also be expanded into an asymptotic series. To obtain...

k}p^{k}(1-p)^{n-k}\simeq {\frac {\lambda ^{k}e^{-\lambda }}{k!}}.} Using Stirling's approximation, it can be written: ( n k ) p k ( 1 − p ) n − k = n ! ( n − k )...

numerator of the fraction would grow singly exponentially while by Stirling's approximation the denominator grows more quickly than singly exponentially),...