Asymptotic expansions for certain mathematical constants and special functions

Abstract

n k=1 b k k −α. Abel proved that S [α] b (n) ∼ b n ∞ k=0 c k n −(k+α) (n → ∞), and gave an explicit formula for determining the coefficients c k ≡ c k (b, α) in terms of Stirling numbers of the second kind. We here provide a recurrence relation for determining the coefficients c k , without Stirling numbers. We also consider asymptotic expansions concerning Somos' quadratic recurrence constant, Glaisher-Kinkelin constant, Choi-Srivastava constants, and the Barnes G-function.

Some new properties of the Barnes G-function and related results

“…Quite recently, Chen [11] made use of the Stirling formula (1.10) in order to develop a complete asymptotic expansion given by…”

“…Chen [9] and [32] dealt with the problem of approximating and finding asymptotic expansions related to the Glaisher-Kinkelin constant A and the Choi-Srivastava constants B and C. Subsequently, Cheng and Chen [17] as well as Chen and Choi [12] established new asymptotic expansions of the Glaisher-Kinkelin A and the Choi-Srivastava constants B and C. on the other hand, by using the Bernoulli numbers B n , Chen [9] established the asymptotic expansions related to the constants A, B and C. More recently, Chen [11] presented a recurrence relation for determining the coefficients of the asymptotic expansion related to each of the constants A, B and C, without using the Bernoulli numbers B n .…”

Bifurcation analysis and control study of improved full-speed differential model in connected vehicle environment

“…The microscopic model mainly studies the state of rear vehi-cles following the front vehicle in a single lane in a queue. In the process of simulating the movement of a single vehicle on an urban road, a variety of factors have been considered such as vehicle performance and inter-vehicle interactions, [1][2][3] the influence of driver behavior and attributes, [4,5] the influence of pavement quality and road conditions, [6][7][8] the influence of the information environment and weather conditions, [9,10] etc. The models have been established, and simulations and analyses have been carried out.…”

Asymptotic expansions for the Wallis sequence and some new mathematical constants associated with the Glaisher-Kinkelin and Choi-Srivastava constants

“…Recently, Chen [17] derived a recurrence relation for determining the coefficients of each asymptotic expansion related to the constants A, B and C, without using the Bernoulli numbers B n . More precisely, Chen [17] proved the following results:…”