An approximation for n! using Stirling’s formula

نویسنده

  • Vinod Viswanath
چکیده

In this paper, an approximation for n! (given by Stirling’s formula) is calculated. The accuracy of this formula is also presented. Some improvisations on the accuracy are explored.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Laplace’s Method, Fourier Analysis, and Random Walks on Z

1.1. Stirling’s formula. Laplace’s approach to Stirling’s formula is noteworthy first, because it makes a direct connection with the Gaussian (normal) distribution (whereas in other approaches the Gaussian distribution enters indirectly, or not at all), and second, because it provides a general strategy for the asymptotic approximation of a large class of integrals with a large parameter. Stirl...

متن کامل

Stirling’s Formula Revisited via Some Classical and New Inequalities

The Hermite-Hadamard inequality is used to develop an approximation to the logarithm of the gamma function which is more accurate than the Stirling approximation and easier to derive. Then the concavity of the logarithm of gamma of logarithm is proved and applied to the Jensen inequality. Finally, the Wallis ratio is used to obtain the additional term in Stirling’s approximation formula. Mathem...

متن کامل

Chapter 1 Stirling ’ s Formula

How do the two most important fundamental constants of mathematics, e and π, find their way into an asymptotic formula for the product of integers? We give two very different arguments (one will not show the full formula) that, between them, illustrate a good number of basic asymptotic methods. The formal language of Asymptopia, such as o(n) and O(n), is deferred to Chapter 2. Two further argum...

متن کامل

New asymptotic expansion for the Γ (x) function

Using a series transformation, Stirling-De Moivre asymptotic series approximation to the Gamma function is converted into a new one with better convergence properties. The new formula is compared with those of Stirling, Laplace and Ramanujan for real arguments greater than 0.5 and turns out to be, for equal number of ’correction’ terms, numerically superior to all of them. As a side benefit, a ...

متن کامل

Networks and Random Processes, MathSys MA933, 2016

(a) Consider a sequence of independent coin tosses with P[heads] = p and let Yn be the number of heads up to time n with Y0 = 0. Give the state space S and transition matrix for the process (Yn : n ∈ N0). Compute P[Yn = k] for all n, k ≥ 0 using the binomial formula. (b) Let (Zn : n ∈ N0) be a simple random walk on S = Z with transition matrix p(x, y) = pδy,x+1 + qδy,x−1. Use that Zn = 2Yn − n ...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2007