Conjecture concerning a completely monotonic function

Details Conjecture concerning a completely monotonic function Conjecture concerning a completely monotonic function

2010-06-07

arxiv.org/abs/1006.1374v1

Mathematics

Classical Analysis and ODEs

accepted for publication in Computers and Mathematics with Applications

Scientific paper

Based on a sequence of numerical computations, a conjecture is presented
regarding the class of functions $H(x;a)=\exp(a)-(1+a/x)^x$, and the open
problem of determining the values of $a$ for which the functions are completely
monotonic with respect to $x$. The critical value of $a$ is determined here to
sufficient accuracy to show that it is not a simple symbolic quantity.

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