Abstract
We present the history of indefinite summation starting with classics (Newton, Montmort, Taylor, Stirling, Euler, Boole, Jordan) followed by modern classics (Abramov, Gosper, Karr) to the current implementation in computer algebra system Maple. Along with historical presentation we describe several “acceleration techniques” of algorithms for indefinite summation which offer not only theoretical but also practical improvement in running time. Implementations of these algorithms in Maple are compared to standard Maple summation tools.
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