Solving the General Truncated Moment Problem by the r-Generalized Fibonacci Sequences Method

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