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math.CO2011
Formal residue and computer proofs of combinatorial identities
Qing-Hu Hou, Hai-Tao Jin
The coefficient of x^{-1} of a formal Laurent series f(x) is called the formal residue of f(x). Many combinatorial numbers can be represented by the formal residues of hypergeometr…
math.CA2011
The Abel-Zeilberger Algorithm
William Y. C. Chen, Qing-Hu Hou, Hai-Tao Jin
We use both Abel's lemma on summation by parts and Zeilberger's algorithm to find recurrence relations for definite summations. The role of Abel's lemma can be extended to the case…