RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO Serie II, Tomo XLVII! (1999), pp. 591-596 GENERATING FUNCTIONS OF THE INCOMPLETE FIBONACCI AND LUCAS NUMBERS A. PINTER - H. M. SRIVASTAVA For the incomplete Fibonacci and incomplete Lucas numbers, which were introduced and studied recently by P. Filliponi [Rend. Circ. Math. Palermo (2) 45 (1996), 37-56], the authors derive two classes of generating functions in terms of the familiar Fibonacci and Lucas numbers, respectively. 1. Introduction and the Main Result. The incomplete Fibonacci and incomplete Lucas numbers were intro- duced recently by Filipponi [1]. The incomplete Fibonacci numbers Fn(k) are defined by (1) Fn(k)= Z . n = 1,2,3,...;0<k< j=O J and the incomplete Lucas numbers Ln(k) are defined by (2) Ln(k) = ~---~ n n-j n= 1,2,3,...'0<k< j=o n-j j ' '