The {K<inf>i</inf>(z)}<inf>i</inf>^∞=1 functions

Abstract

In this paper we define and study the functions Ki(z)= 1M0(1;1, z + i - 1) - 1M0(1;1, i - 1)/1M-1(1;1,i), i ∈ N, where function vMm(s; a, z) is defined in [9]. We give the recurrence relations, asymptotic and other properties. Also, we give the exponential generating function and representation of Ki(n). Copyright © 2006 Rocky Mountain Mathematics Consortium.