Asymptotic Approximations for n !
نویسنده
چکیده
Several approximations for n! have recently appeared in the literature. We show here how these approximations can be derived by expansion of certain polynomials in inverse powers of n and comparison with Stirling’s asymptotic series. Some new approximations are also given. The same procedure is applied to generate approximations for the ratio of two gamma functions.
منابع مشابه
Asymptotic Approximations of the Solution for a Traveling String under Boundary Damping
Transversal vibrations of an axially moving string under boundary damping are investigated. Mathematically, it represents a homogenous linear partial differential equation subject to nonhomogeneous boundary conditions. The string is moving with a relatively (low) constant speed, which is considered to be positive. The string is kept fixed at the first end, while the other end is tied with the ...
متن کاملMultinomial Expressions Summation Asymptotic Approximations
The asymptotic behaviour with respect to n of sums of type ∑
متن کاملSecond Order Moment Asymptotic Expansions for a Randomly Stopped and Standardized Sum
This paper establishes the first four moment expansions to the order o(a^−1) of S_{t_{a}}^{prime }/sqrt{t_{a}}, where S_{n}^{prime }=sum_{i=1}^{n}Y_{i} is a simple random walk with E(Yi) = 0, and ta is a stopping time given by t_{a}=inf left{ ngeq 1:n+S_{n}+zeta _{n}>aright} where S_{n}=sum_{i=1}^{n}X_{i} is another simple random walk with E(Xi) = 0, and {zeta _{n},ngeq 1} is a sequence of ran...
متن کاملLaplace approximation of Lauricella functions F A and F D
The Lauricella functions, which are generalizations of the Gauss hypergeometric function 2F1, arise naturally in many areas of mathematics and statistics. So far as we are aware, there is little or nothing in the literature on how to calculate numerical approximations for these functions outside those cases in which a simple one-dimensional integral representation or a one-dimensional series re...
متن کاملTwo-Moment Approximations for Maxima
We introduce and investigate approximations for the probability distribution of the maximum of n i.i.d. nonnegative random variables, in terms of the number n and the first few moments of the underlying probability distribution, assuming the distribution is unbounded above but does not have a heavy tail. Since the mean of the underlying distribution can immediately be factored out, we focus on ...
متن کامل