2011/05/01 by William Y. C. Chen, Chen, William Y. C., Qing-Hu Hou +3
Mathematics · Physics and Astronomy · #05A19 #33F10 #39A10 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Advanced Mathematical Theories and Applications #Classical Analysis and ODEs (math.CA) #Combinatorics (math.CO) #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.1105.0178
openalex publication_date 2011/05/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 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, the Apery-Schmidt-Strehl identity, Calkin's identity and some identities involving Fibonacci numbers.