Séminaire Lotharingien de Combinatoire, S43b (2000), 10 pp.

Carsten Schneider

An Implementation of Karr's Summation Algorithm in Mathematica

Abstract. Implementations of the celebrated Gosper algorithm (1978) for indefinite summation are available on almost any computer algebra platform. We report here about an implementation of an algorithm by Karr, the most general indefinite summation algorithm known. Karr's algorithm is, in a sense, the summation counterpart of Risch's algorithm for indefinite integration. This is the first implementation of this algorithm in a major computer algebra system. Our version contains new extensions to handle also definite summation problems. In addition we provide a feature to find automatically appropriate difference field extensions in which a closed form for the summation problem exists. These new aspects are illustrated by a variety of examples.

Received: February 16, 2000; Accepted: February 28, 2000.

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