Unified treatment of several asymptotic expansions concerning some mathematical constants

作者：Chen, Chao-Ping^*; Choi, Junesang

来源：Applied Mathematics and Computation, 2017, 305: 348-363.

DOI：10.1016/j.amc.2017.02.001

• Euler-Mascheroni constant
• Constants of Landau and Lebesgue
• Glaisher-Kinkelin constant
• Choi-Srivastava constants
• Asymptotic expansion

Recently various approximation formulas for some mathematical constants have been investigated and presented by many authors. In this paper, we first find that the relationship between the coefficients p(j) and q(j) is such that @@@ psi (x Sigma(infinity)(j=0) q(j)x(-j)) similar to In (x Sigma(infinity)(j=0) p(j)x(-j)), x -> infinity, @@@ where psi is the logarithmic derivative of the gamma often referred to as psi function) and p(0) = q(0) = 1. Next, by using this result, we give a unified treatment of several asymptotic expansions concerning the Euler-Mascheroni constant, Landau and Lebesgue constants, Glaisher-Kinkelin constant, and Choi-Srivastava constants.

• 出版日期2017-7-15
• 单位河南理工大学