Abstract
In this paper we consider the generalized Marcum Q-function of order ν > 0 real, defined by Q ν ( a , b ) = 1 a ν - 1 ∫ b ∞ t ν e - t 2 + a 2 2 I ν - 1 ( at ) dt , where a > 0, b ⩾ 0 and I ν stands for the modified Bessel function of the first kind. Our aim is to extend some results on the (first order) Marcum Q-function to the generalized Marcum Q-function in order to deduce some new lower and upper bounds. Moreover, we show that the proposed bounds are very tight for the generalized Marcum Q-function of integer order, and we deduce some new inequalities for the more general case of real order. The chief tools in our proofs are some monotonicity properties of certain functions involving the modified Bessel function of the first kind, which are based on a criterion for the monotonicity of the quotient of two Maclaurin series.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
