The programming language MAPLE uses different algorithms to find closed forms for symbolic indefinite summations. MAPLE does not explicitly contain a procedure to interchange the order, and resultantly will give up on many summations which could be solved by interchanging the order of summation. In this project we look into the task of interchanging the order of summation over a specific domain, and provide a MAPLE procedure which automates this task. We then look into identities involving harmonic numbers which we derive through this new procedure, existing MAPLE summation techniques and user manipulation. We then analyze the well known algorithm Quicksort using these identities. Lastly, we look into the summation procedure by Moenck which is used for rational function summations.
Worcester Polytechnic Institute
Major Qualifying Project
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