Monotonicity patterns and functional inequalities for the Nuttall Q-function

In this paper, we prove the monotonicity property of ratios for the Nuttall Q-function. As a direct consequence, the monotonicity properties of ratios for the generalized Marcum Q-function and the confluent hypergeometric function are derived. Next, new bounds for the Nuttall Q-function are established. In particular, new bounds for the generalized Marcum Q-function are presented. Furthermore, numerical computations and graphical representations are discussed.