A novel representation for the Nuttall Q-function

The aim of this work is the derivation of a novel explicit representation for the Nuttall Q-function, Q_m,n(a,b). The Nuttall Q-function is a relatively new special function. Its usefulness in wireless communications is evident by its utilization in applications related to the field of digital communications over fading channels. It is denoted as Q_m,n(a,b) and it was first proposed by A. H. Nuttall,as a generalisation of the Marcum Q-function, Q_m(a,b). Consequently, M. K. Simon derived, a closed-form expression for Q_m,n(a,b) in terms of Q_m(a,b) and the modified Bessel function of the first kind, l_n(x). This representation has a finite series form and is valid only for the case that the sum of its two order indices -m + n- is an odd integer.