Geodesic
The Abel-Zeilberger algorithm
The electronic journal of combinatorics, The Zeilberger Festschrift volume, Tome 18 (2011) no. 2
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By combining Abel's lemma on summation by parts with Zeilberger's algorithm, we give an algorithm, called the Abel-Zeilberger algorithm, to find recurrence relations for definite summations. The role of Abel's lemma can be extended to the case of linear difference operators with polynomial coefficients. This approach can be used to verify and discover identities involving harmonic numbers and derangement numbers. As examples, we use the Abel-Zeilberger algorithm to prove the Paule-Schneider identities, an identity of Andrews and Paule, and an identity of Calkin.
DOI : 10.37236/2013
Classification : 33F10, 68W30, 05A19, 39A10
Mots-clés : symbolic summation, hypergeoemtric sequences, holonomic sequences 
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William Y.C. Chen; Qing-Hu Hou; Hai-Tao Jin. The Abel-Zeilberger algorithm. The electronic journal of combinatorics, The Zeilberger Festschrift volume, Tome 18 (2011) no. 2. doi: 10.37236/2013

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