  In 1993 one of the authors formulated some conjectures on monotonicity of
ratios for exponential series sections. They lead to more general conjecture on
monotonicity of ratios of Kummer hypergeometric functions and was not proved
from 1993. In this paper we prove these conjectures in the more general setting
for Kummer hypergeometric functions and its further generalizations for Gauss
and generalized hypergeometric functions. The results are also closely
connected with Turan--type inequalities.
