Solving the general truncated moment problem by the r-generalized Fibonacci sequences method

Abstract

We give in this paper a new method for solving the generalized truncated power moment problem. To this aim we use r-generalized Fibonacci sequences and their associated minimal polynomials. We provide an algorithm of construction of solutions in a short method. This method allows us to avoid any appeal to Hankel matrices or any positive definiteness conditions as in the Flessas-Burton-Whitehead (FBW) approach. Examples and general cases are discussed. © 2001 Academic Press.