  Some sharp two-sided Tur\'an type inequalities for parabolic cylinder
functions and Tricomi confluent hypergeometric functions are deduced. The
proofs are based on integral representations for quotients of parabolic
cylinder functions and Tricomi confluent hypergeometric functions, which arise
in the study of the infinite divisibility of the Fisher-Snedecor F
distribution. Moroever, some complete monotonicity results are given concerning
Tur\'an determinants of Tricomi confluent hypergeometric functions. These
complement and improve some of the results of Ismail and Laforgia [23].
