New representations for the Lugo and Euler-Mascheroni constants

作者：Chen, Chao-Ping; Srivastava, H. M.^*

来源：Applied Mathematics Letters, 2011, 24(7): 1239-1244.

DOI：10.1016/j.aml.2011.02.015

• Euler Mascheroni constant and the Gamma function
• Weierstrass formula
• Lugo's constant
• Psi (or Digamma) function
• Arithmetical functions
• Speed of convergence and approximation

Lugo's constant L given by
L = -1/2 - lambda + ln 2
is defined as the limit of the sequence (L(n))(n epsilon N) defined by
Ln := Sigma(n)(i=1)Sigma(n)(j=1) 1/i+j - (2 ln 2)n + ln n (n epsilon N)
as n -> infinity, N being the set of positive integers. In this paper, we establish new analytical representations for the Euler-Mascheroni constant gamma in terms of the psi function. We also give the bounds of L-L(n) and present a new sequence which converges to Lugo's constant L.

• 出版日期2011-7
• 单位河南理工大学