New bounds and asymptotic expansions for the constants of Landau and Lebesgue

作者：Chen, Chao-Ping^*

来源：Applied Mathematics and Computation, 2014, 242: 790-799.

DOI：10.1016/j.amc.2014.06.078

• Constants of Landau and Lebesgue
• Gamma function
• Psi function
• Inequality
• Asymptotic expansion
• Stirling numbers of the second kind

The constants of Landau and Lebesgue are defined, for all integers n >= 0, in order, by
Gn = Sigma(n)(k-0)1/16(k)(k(2k))(2) and L-n = 1/2 pi integral(pi)(-pi)vertical bar sin((n+1/2)t)/sin(1/2t)vertical bar dt,
which play important roles in the theories of complex analysis and Fourier series, respectively. In this paper, we establish new bounds and asymptotic expansions for the constants of Landau and Lebesgue.

• 出版日期2014-9-1
• 单位河南理工大学