Symbolic computation and positivity of holonomic sequences

Symbolic computation and positivity of holonomic sequences (Advisor: Veronika Pillwein). Around ten years ago Stefan Gerhold and Manuel Kauers developed a symbolic method to show positivity for sequences defined by a linear recurrence relation with polynomial coefficients. More recently, in the course of a termination analysis, a variation of this method has been introduced. The goal of this thesis is to implement this new procedure in Mathematica and compare its behaviour at some practical examples with the existing implementation of the Gerhold-Kauers method.

Around ten years ago Stefan Gerhold and Manuel Kauers developed a symbolic method to show positivity for sequences defined by a linear recurrence relation with polynomial coefficients. More recently, in the course of a termination analysis, a variation of this method has been introduced. The goal of this thesis is to implement this new procedure in Mathematica and compare its behaviour at some practical examples with the existing implementation of the Gerhold-Kauers method.