S. M. Sitnik
Published 2012-07-04, updated 2014-10-29Version 3
In the preprint of 1993 the author formulated some conjectures on monotonicity of ratios for exponential series remainders. They are equivalent to conjectures on monotonicity of a ratio of Kummer hypergeometric functions and presumably not proved still. In this short note the most interesting conjecture from the preprint of 1993 is reproduced with its generalizations. In the updated version an important information is added that conjectures 1, 2 and also problems 1, 2 were recently proved by Khaled Mehrez from IPEIM, Tunisia, for details cf. arXiv:1410.6120v2.
Asymptotic expansions of Kummer hypergeometric functions for large values of the parameters
Proofs of some conjectures on monotonicity of ratios of Kummer, Gauss and generalized hypergeometric functions
Asymptotic expansions of Kummer hypergeometric functions with three asymptotic parameters $a$, $b$ and $z$
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