Tight bounds for the generalized Marcum Q-function

In this paper we study the generalized Marcum Q  -function of order ν>0ν>0 real, defined byQν(a,b)=1aν−1∫b∞tνe−t2+a22Iν−1(at)dt, where a>0a>0, b⩾0b⩾0 and IνIν stands for the modified Bessel function of the first kind. Our aim is to improve and extend some recent results of Wang to the generalized Marcum Q  -function in order to deduce some sharp lower and upper bounds. In both cases b⩾ab⩾a and b