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Summations can really get complicated - esp. when you have convoluted n-fold summations with all kinds of different indices.

My question: Is there some software (or add-on) with which you can find and prove (complicated) summation identities?

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Implementations of Gosper's algorithm and related work (e.g. Zeilberger's algorithm and Petkovšek's algorithm). –  Peter Taylor Jan 25 '11 at 11:04
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Mathematica does it reasonably well. If you derived one sum from the other, then evaluate the sums for a large amount of values should give you enough confidence that the 2 are equal. –  Chao Xu Jan 25 '11 at 11:04
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up vote 2 down vote accepted

Fabrizio Caruso implemented "Gosper's and Zeilberger's algorithm for proving and finding indefinite and definite hypergeometric summation identities", as a free and open source package for use with Maxima. You can get it here.

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