On an infinite series for $(1+1/x)^x$
  The aim of this paper is to construct a new expansion of $(1+1/x)^x$ related to Carleman's inequality. Our results extend some results of Yang [Approximations for constant e and their applications J. Math. Anal. Appl. 262 (2001) 651-659]. 
Cristinel Mortici and Yue Hu
math.CA