Asymptotic expansions for the constants of Landau and Lebesgue

作者：Chen, Chao-Ping^*; Choi, Junesang

来源：Advances in Mathematics, 2014, 254: 622-641.

DOI：10.1016/j.aim.2013.12.021

• Constants of Landau and Lebesgue
• Gamma function
• Psi function
• Asymptotic expansion
• Stirling numbers of the second kind
• Bernoulli numbers and polynomials
• Bell polynomials
• Partition function

The constants of Landau and Lebesgue are defined, for all integers n >= 0, in order, by
G(n) = Sigma(n)(k=0) 1/16(k) ((2k)(k))(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. Certain inequalities and asymptotic expansions for the constants G(n) and L-n, been investigated by many authors. Here we aim at establishing new asymptotic expansions for the constants G(n) and L-n of Landau and Lebesgue, respectively, by mainly using Bell polynomials and the partition function.

• 出版日期2014-3-20
• 单位河南理工大学