Accurate estimates of (1+x)^{1/x} Involved in Carleman Inequality and Keller Limit

Branko Malesevic, Yue Hu, Cristinel Mortici


In this paper, using the Maclaurin series of the functions $(1+x)^{1/x}$, some inequalities from papers Bichen-Debnath [1998] and Mortici-Jang [2015] are generalized. For arbitrary Maclaurin series some general limits of Keller's type are defined and applying for generalization of some well known results.

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