Given that m ranges over -10.10 the expression m+11 will range over 1.21. Further reproduction, or any copying of machine-readable files (including this one) to any server computer, is strictly prohibited. the call returns a list of values and the expression m+11 selects the m-plus-11-th element of the list the doubled square brackets are a short-hand for Mathematicas Part function. Karr’s algorithm is, in a sense, the summation counterpart of Risch’s algorithm for indefinite integration. We report here about an implementation of an algorithm by Karr, the most general indefinite summation algorithm known. Permission is hereby granted for web users to make one paper copy of this page for their personal use. Implementations of the celebrated Gosper algorithm (1978) for indefinite summation are available on almost any computer algebra platform. To order Mathematica or this book contact Wolfram Research: 1-80. Gosper::usage = "Gosper]] pn = 1 rnj = Expand] res = Resultant Web sample page from The Mathematica Book, First Edition, by Stephen Wolfram, published by Addison-Wesley Publishing Company (hardcover ISBN 4-5 softcover ISBN 0-2). The algorithm is in some respects analogous to the Risch algorithm that Mathematica uses for indenite integration.
This algorithm can take sums whose successive terms have ratios which are rational functions, and can nd explicit formulae for sums in terms of rational and other functions.
A.2 Implementing Mathematical Algorithms 623 A.2.6 Symbolic Summation As a nal example of the implementation of mathematical algorithms in Mathematica, we consider a somewhat more complicated example: Gosper's algorithm for nding closed-form results for symbolic sums.
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